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Chapter 2. Measurements and Calculations

- Making observations is a key part of the scientific process.
- Sometimes observations are qualitative and sometimes they are quantitative.
- A measurement is a quantitative observation.
- It's very important to measure in our daily lives.
- The gas pump has to accurately measure the gas delivered to the fuel tank because we pay by the gallon.
- The amount of oxygen in the exhaust gases, the temperature of the coolant, and the pressure of the lubricating oil are some of the variables that affect the efficiency of the modern automobile engine.
- Cars with traction control systems can measure and compare the rates of rotation of all four wheels.
- In the "Chemistry in Focus" discussion in this chapter, we will see that measuring devices have become very sophisticated in dealing with our fast- moving and complicated society.

- A measurement consists of a number and a unit.
- The measurement needs both parts to be meaningful.
- Suppose a friend tells you that she saw a bug.
- As it stands, this statement is meaningless.
- The bug is small if it's 5 millimeters.
- The bug is large if it's 5 centimeters.

- For a measurement to be meaningful, it must include both a number and a unit that tells us the scale being used.

- In this chapter, we will look at the characteristics of measurements and the calculations that involve them.

- The amount of gasoline delivered is measured by a gas pump.

- To show how the product of a number between 1 and 10 and a power of 10 can be expressed.

- The numbers associated with scientific measurements can be large or small.
- The distance from the earth to the sun is 93 million miles.
- This number is large.
- Scientific notation can be used to make large numbers more compact and easier to write.

- A measurement must always include a number and a unit.

- A number in the form Nx10M is a convenient method for representing a large or small number and for easily indicating the number of significant figures simply expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

- It is convenient to use scientific notation when describing very small distances.

- The easiest way to determine the appropriate power of 10 is to start with the number being represented and count the number of places the decimal point must be moved to get a number between 1 and 10.

- To make up for every move of the decimal point to the left, we must use 10.
- We make the number smaller by one power of 10 when we move the decimal point to the left.
- For each move of the decimal point to the left, we need to add 10 to restore the number to its original magnitude.

- To the left of the decimal point, keep one digit.

- A positive exponent is needed to move the decimal point to the left.

- The exponent of 10 is positive when the decimal point is moved to the left.

- The power of 10 is negative, so we can represent numbers smaller than 1 by using the same convention.

- This requires an equation of 1.0x10-2.
- The exponent of 10 is negative when the decimal point is moved to the right.

- A negative exponent is needed to move the decimal point to the right.

- The number 0.000167 is considered.

- The exponent of -4 is needed to move the decimal point four places to the right.

- If you need a further discussion of scientific notation, read the Appendix.

- The procedures are summarized below.

- The product of a number between 1 and 10 and a power of 10 can be represented.
- The power of 10 depends on the number of places the decimal point is moved.
- The power of10 is determined by the number of places the decimal point is moved.
- The power of 10 is determined by the direction of the move.
- The power of 10 is positive if the decimal point is left or right.

- The numbers should be represented in scientific notation.

- When written in scientific notation, a number greater than 1 will always have a positive exponent.

- The power of 10 is positive 5 because we moved the decimal point five places to the left.

- The numbers should be represented in scientific notation.

- A number that is less than 1 will always have a negative exponent.

- The power of 10 is negative 4 because we moved the decimal point four places to the right.

- Problems 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11 and 2.12 can be seen.

- To learn the English, metric, and SI systems of measurement.

- The part of a measurement that tells us what scale is being used to represent the results is called a unit.
- The English system tells us what scale or standard is being used to represent the results of the measurement.
- Common units have been required for trade from the earliest days of civilization.
- If a farmer from one region wanted to trade some of his grain for the gold of a miner who lived in another region, the two people had to have common standards for measuring the amount of the grain and the weight of the gold.

- Scientists who measure quantities such as mass, length, time, and temperature need to use common units.
- Chaos would result if every scientist had his or her own units.
- Different systems were adopted in different parts of the world despite standard systems of units.
- The English system and the metric system are used most in the industrialized world.

- Most scientific work uses the metric system.
- SIInternational System of units based on the metric system and units derived from the metric system was established in 1960 by an international agreement.
- The SI units are derived from the metric system.
- Table 2.1 contains the most important fundamental SI units.
- We will discuss how to manipulate some of these units later in the chapter.

- NASA lost $125 million because of a failure to convert from English to metric units.

- Two teams working on the Mars mission were using different units.
- NASA's scientists at the Jet Propulsion Laboratory assumed that the thrust data for the rockets on the Orbiter were in metric units.
- The units were English.
- The craft burned up because it dipped 100 kilometers lower into the atmosphere than planned.

- The debate over whether Congress should require the United States to switch to the metric system was revived by NASA's mistake.
- Almost all of the world uses the metric system, and the United States is about to switch from English to metric.
- We buy our soda in 2-liter bottles when we are in the automobile industry.

- It's important that units are important.
- They can mean the difference between life and death.
- A Canadian jetliner almost ran out of fuel in 1983, when someone pumped 22,300 pounds of fuel into the aircraft instead of 22,300 kilograms.

- The SI system uses prefixes to change the size of the unit because it is not always convenient.
- Table 2.2 contains the most commonly used prefixes.
- The decimeter is one-tenth of a meter, the cm is one-hundredth of a meter, and the millimeter is one-hundredth of a meter.
- It's easier to specify the diameter of a contact lens as 1.0 cm than it is to specify it as 1.0x10-2 m.

- Both a number and a unit are important in measuring.
- You wouldn't report a measurement without a unit, just as you wouldn't report a measurement without a numerical value.
- You already use units in your daily life, whether you tell someone, "Let's meet in one hour" or you and your friends order two pizzas for dinner.

- The metric system is used to measure length, volume, and mass.

- The powers of 10 can be used to express fractions of a meter or multiples of a meter.

- The English and metric systems are compared on a ruler.

- Section 2.6 contains English-metric equivalencies.

- Amount of three-dimensional space is the amount of space occupied by a substance.
- The volume of a cube that measures 1 meter in each of the three directions is the fundamental unit of volume in the SI system.
- Each edge of the cube is 1 meter in length.

- This cube is divided into 1000 smaller cubes in Figure 2.2.

- The heart of science is measurement.
- We get the data for testing theories by measuring.
- If our drinking water is safe, whether we are anemic or not, and the exact amount of gasoline we put in our cars at the filling station are all important things to know.

- New measuring techniques are being developed every day to meet the challenges of our increasingly sophisticated world, despite the fact that the fundamental measuring devices we consider in this chapter are still widely used.
- Modern automobiles have oxygen sensors that analyze the oxygen content in the exhaust gases.
- instantaneous adjustments can be made in spark timing and air-fuel mixture to provide efficient power with minimum air pollution, if this information is sent to the computer that controls the engine functions.

- A pollution control officer is near a river.

- Paper-based measuring devices are being developed in a recent area of research.
- A nonprofit organization called Diagnostics for All in Cambridge, Massachusetts has invented a paper-based device to detect proper liver function.
- In this test, a drop of the patient's blood is placed on the paper, and the resulting color that develops can be used to determine whether the person's liver function is normal, worrisome, or requires immediate action.
- One of the paper-based measuring devices used to detect counterfeit pharmaceuticals is also used to detect whether someone has been immunized against a specific disease.
- Paper-based devices are especially useful in developing countries because of their affordability.

- Many organisms are sensitive to tiny amounts of chemicals in their environments, so scientists are looking at the natural world to find supersensitive detectors.
- One of these natural measuring devices uses the sensory hairs from Hawaiian red swimming crabs, which are connected to electrical analyzers and used to detect hormones down to levels of 10-8 g/L.
- Similar to pineapple cores, tissues can be used to detect hydrogen peroxide.

- The detection of all kinds of substances in our food and drinking water scares us because of the advances in measuring devices.
- We didn't worry about these substances when we couldn't detect them.
- Risk assessment has become more complex because of the increased sophistication of taking measurements.

- The unit of volume used in chemistry is called a milliliter.
- The relationship is summarized in Table 2.4.

- The graduated cylinder is marked off in convenient units of volume.
- The graduated cylinder can be filled with liquid and poured out.

- Mass is the quantity of matter present in an object.
- The kilogram is the fundamental SI unit of mass.

- The gram is used as the fundamental unit in the metric system, so the prefixes for the various mass units are based on it.

- Balance is used in the laboratory to determine the mass of an object.
- The mass of the object is compared to a set of weights.
- A single-pan balance can be used to determine the mass of an object.

- An electronic balance is used in chemistry labs.

- Some familiar objects are described in Table 2.6 in order to give you a feeling for the common units of length, volume, and mass.

- Understanding how uncertainty arises in a measurement.
- To learn to use significant figures to indicate a measurement's uncertainty.

- The measurement is exact when you count it.
- If you asked your friend to buy you four apples from the store, she would come back with three or five apples, you would be surprised.
- It's not always exact.
- An estimate is required when a measurement is made with a device such as a ruler.
- The pin shown in Figure 2.5(a) can be used to illustrate this.
- From the ruler, we can see that the pin is a little longer and a little shorter.
- Because there are no graduations on the ruler, we have to estimate the pin's length.
- Imagine that the distance between 2.8 and 2.9 is broken into 10 equal divisions and that the end of the pin is one of the 10 equal divisions.
- 5 of our 10 imaginary divisions correspond to the end of the pin coming about halfway between 2.8 and 2.9.
- The pin's length is estimated at 2.85 cm.
- We had to use a visual estimate to calculate the pin's length, so it could be either 2.84 or 2.86 cm.

- A student is in a lab.

- A pin is being measured.

- When another person makes the same measurement, it may be different because the last number is based on a visual estimate.

- The first two digits of each measurement are the same regardless of who made the measurement, these are called the certain numbers of the measurement.
- The third digit can be estimated and can be called an uncertain number.
- The custom is to record all of the numbers plus the first uncertain number when making a measurement.
- This ruler requires an estimate of even the second decimal place, so it would not make sense to measure the pin to the third decimal place.

- A measurement always has some degree of uncertainty.
- The measuring device has an effect on the uncertainty of a measurement.
- If the ruler in Figure 2.5 had marks indicating hundredths of a centimeter, the uncertainty in the measurement of the pin would be in the thousandths place, rather than the hundredths place.

- The first uncertain digit of a measurement and the certain digits are called significant figures.
- The number of significant figures is determined by the uncertainty of the measuring device.
- The ruler used to measure the pin can only give a hundredths of a centimeter results.
- We give information about the uncertainty in a measurement when we record the significant figures.
- Unless otherwise stated, the uncertainty in the last number is usually assumed to be +-1.
- The symbol +- means plus or minus in the case of the measurement 1.86 kilograms.

- To figure out the number of significant figures in a calculation.

- Any measurement that involves an estimate is uncertain to some extent.
- We show the degree of certainty by the number of figures we record.

- We have to consider what happens when we use numbers that contain uncertainties in chemistry calculations.
- We need to know the degree of uncertainty in the final result.
- Although we will not discuss the process here, mathematicians have studied how uncertainty accumulates and have designed a set of rules to determine how many significant figures the result of a calculation should have.
- Whenever you do a calculation, you should follow these rules.
- Learning how to count the significant figures in a given number is the first thing we need to do.

- Significant figures are always counted as nonzero integers.
- The number 1457 has four nonzero integers that count as significant figures.
- Leading zeros are zeros that precede all of the nonzero digits.
- They don't count as significant figures.
- The position of the decimal point is indicated by the three zeros.
- The number has two significant figures, the 2 and the 5.
- They are always significant figures.
- The number 1.008 has four significant figures.Math Skill Builder Captive zeros are always significant figures.Trailing zeros are at the right end of the number.
- If the number is written with a decimal point, they are significant.
- The number one hundred written as 100 has only one significant figure, but it is written as 100.
- Many calculations involve numbers that are not obtained using measuring devices but are determined by counting: 10 experiments, 3 apples, 8 molecules.
- The numbers are called exact numbers.
- It is assumed that they have an unlimited number of significant figures.
- The numbers can come from definitions.
- 1 inch is defined as 2.54 centimeters.

- Rules for counting significant figures can also be applied to numbers written in scientific notation.
- The number of significant figures can be easily indicated, and fewer zeros are needed to write a large or a small number in scientific notation.
- The number is represented as 6.0x10-5 and there are two significant figures written in either form.

- Significant figures are easy to see.

- Give the number of significant figures for each measurement.

- A forensic chemist in a crime lab weighs a single hair and records its mass as 5000 g. Only 60 riders finished yesterday's bicycle race.

- There are three significant figures in the number.
- The zeros to the left of the 1 are not significant, but the remaining zero is significant.
- There are five significant figures in the number.
- The leading zeros are not significant.
- The trailing zero to the right of the 6 is significant because the number has a decimal point.
- There are four significant figures in this number.
- The zeros in 5.030 are significant.
- The numbers were obtained by counting the riders.
- There is an unlimited number of significant figures in these numbers.

- Give the number of significant figures for each measurement.
- The leading zeros to the left of the 1 do not count, but the trailing zeros do.
- An exact number is obtained by counting the cars.
- There is an unlimited number of significant figures.

- Problems 2.33 and 2.34 can be seen.

- The number of digits displayed on the calculator is usually more than the number of significant figures that the result should have.
- Reducing the number to fewer digits is what you must do.
- There are rules for rounding off.

- The preceding digit stays the same if the digit is less than 5.
- The preceding digit is increased by 1 if 1.33 rounds to 1.3 is equal to or greater than 5.
- Carry the extra digits through to the final result in a series of calculations.
- If you want to use the procedures in Rule 1 to round off, you should carry all of the digits that show on your calculator until you arrive at the final number.

- The correct number of significant figures needs to be rounded off.
- The number needs to be rounded to two significant figures.

- The number is rounded to 4.3 because it is less than 5.
- Do not round the 4 to 5 to give 4.35 and then round the 3 to 4 to give 4.4.

- Don't round off.
- 6.84 is not the number that was rounded to three significant figures.

- The first number should be used when rounding off.

- We will learn how to determine the correct number of significant figures from a calculation.
- The following rules will be used to do this.

- The number of significant figures in the result is the same as the number of significant figures in the measurement.
- The number of significant figures in the result is limited by this measurement.
- The result is limited to two significant figures because 1.4 has only two significant figures.
- The product is correctly written as 6.4, which has two significant figures.
- Consider another example.
- The answer is limited by the number of significant figures in the division.
- The limiting term is the one with the smallest number of decimal places.
- An uncertain number is the last digit reported in a measurement.
- The same quantities are treated by your calculator, but they are different to a scientist.

- Significant figures are counted for multiplication and division.
- The decimal places are counted for addition and subtraction.

- The things you have learned about significant figures will be put together by considering some mathematical operations.

- If you don't perform the calculations, tell how many figures each answer should have.

- The answer will have a single digit.
- The answer has two significant figures because the limiting number is 1.9.
- The answer won't have digits after the point.
- The answer has four significant figures because the number 1081 has no digits to the right of the decimal point.
- There are only two significant figures in the answer because of the number 2.3.
- There will be three significant figures in the answer.
- 3 boxes of candy is an exact number, so the limiting factor is 2.50.

- Give each result to the correct number of significant figures using the following mathematical operations.

- The result should have two significant figures if 4.3 has the least number of significant figures.
- Before rounding the answer to the correct number of significant figures, we perform all calculations.
- The answer must have no digits after the decimal point.
- The digit to the right is greater than 5 so the 4 is rounded up to 5.
- We round the first answer from the first operation before performing the next one.
- We don't know the correct number of places.

- We rounded the result to the correct number of significant figures so that we would know the correct number of decimal places.

There are Problems 2.47, 2.48, 2.49, 2.50, 2.51 and 2.52

- To learn how multidimensional analysis can be used to solve problems.

- If the boss at the store where you work asks you to pick up 2 dozen doughnuts on the way to work, you should do it.
- The shop sells by the doughnuts.

- This is an example of a problem where you have to convert from one unit of measurement to another.
- The recipe calls for 3 cups of cream, which is sold in pints.

- Let's use the doughnut problem to explore this process.

- You have to buy 24 doughnuts.

- The conversion factor is a ratio of the two parts of the definition.
- The unit cancels.

- Let's generalize a bit.
- The conversion factor will be used to change from one unit to another.

- The conversion factor is the ratio of the two parts of the statement.
- In the following discussion, we will see more about this.

- We considered a pin that was more than 2 cm in length.

- The number we want to find is the question mark.
- We need to know the relationship between inches and centimeters to solve this problem.

- A statement that relates different units of measurement is called an equivalence statement.
- The numbers refer to different scales for distance.

- The conversion factors are the ratios of the two parts of the equivalence statement.

- We choose a conversion factor that cancels the units we want to discard and leaves the units we want in the result.

- Units cancel the same way as numbers do.

- The inches are given by the centimeter units.
- The value is the same as the length.
- The number decreased from 2.85 to 1.12.
- The inch is a bigger unit of length than the centimeter is.
- It takes less inches to make the same length.
- Make sure that the answer makes sense when you finish a calculation.

- There are three significant figures required for the conversion.
- You might think that the result should have only one significant figure because the term 1 appears in the conversion.
- The answer should be 1 in.
- The number of significant digits in the result is not limited by the 1

- When exact numbers are used, they don't limit the number of significant digits.

- We've seen how to convert from one size to another.
- A pencil is 7.00 in.

- There are two conversion factors that can be derived from each equivalence statement.

- We look at the direction of the required change to choose which factor to use.
- The inches must be canceled for us to change from inches to centimeters.

- The inch units are no longer required.

- The number increased in this conversion.
- The inch is a larger unit of length than the centimeter.
- It takes more centimeters to make the same length.
- Do you think your answer makes sense?
- You will be able to avoid errors.

- Changing from one unit to another via conversion factors is called a "dimensional analysis."
- This method will be used throughout the study of chemistry.

- There are some general steps for doing conversions.

- If you want to convert from one unit to another, use the equivalence statement.
- The ratio of the two parts of the equivalence statement is the conversion factor.

- Make sure the unwanted units cancel if you choose the appropriate conversion factor.

- To give the quantity with the desired units, multiply the quantity to be converted by the conversion factor.

- Make sure you have the correct number of figures.

Do you think your answer makes sense?

- This procedure will be shown in example 2.6.

- The frame size of the Italian bicycle is 62 cm.

- We want to convert from centimeters to inches.

- The result is limited to two figures.
- The centimeters are no longer required.

- The number decreased in this conversion.
- The inch is a larger unit of length than the centimeters.

- Wine is usually bottled in 0.750-L containers.

- Problems 2.59 and 2.60 can be seen.

- A conversion that requires several steps will be considered next.

- The marathon is a long race.

- The process will be done one conversion at a time to make sure everything is clear.

- The marathon is 42.1 km.

- You can combine the steps if you feel comfortable with the conversion process.

- The correct number of significant figures will be shown at the end of each step.
- If you are doing a multistep calculation, you should keep the extra numbers on your calculator and round them off at the end of the calculation.

- The result has three significant figures because the units cancel to give the required kilometers.

- Racing cars travel around the track at an average speed of over 200 miles per hour.

- Problems 2.65 and 2.66 can be seen.

- A measurement has two parts, a number and a unit.
- Units are used to check the validity of your solution.
- Always use them.
- As you carry out the calculations, cancel units.
- The final answer has the correct units.
- You have done something wrong if it doesn't happen.
- The final answer has the correct number of significant figures.
- Do you think your answer makes sense?

- To learn the temperature scales.
- To learn how to change from one scale to another.
- To develop problem-solving skills.

- The weather person on TV says it will be 75 degrees tomorrow and the doctor tells you your temperature is 102 degrees.
- In the United States and Great Britain, the temperature scale is used in most engineering sciences.
- In Canada and Europe, the Celsius scale is used in the physical and life sciences.
- The unit of temperature is called a degree and is followed by the capital letter of the scale on which the units are measured.

- The absolute scale is used in the sciences.

- It is more correct to say 373 kelvins than 373 K.

- The temperature scales are compared.
- There are a lot of important facts.

- The temperature scales are ice water and boiling water.

- The size of each degree is the same for the scales.
- The difference between the boiling and freezing points of water is 100 units on both scales.
- The degree is smaller than the other units.
- The difference between the boiling and freezing points of water on the Fahrenheit scale is 180 degrees, compared with 100 units on the other two scales.
- On all three scales, the zero points are different.

- You will need to convert from one temperature scale to another in chemistry.
- How this is done will be considered in some detail.
- In addition to learning how to change temperature scales, you should use this section to further develop your skills in problem solving.

- The temperature unit is the same size as the zero points, so it is easy to convert between the scales.
- This procedure will be shown in example 2.8.

- There is a boiling point at the top of the mountain.

- Chapter 14 will discuss boiling points further.

- It is helpful to draw a diagram in which we try to represent the words in the problem with a picture.
- The problem can be shown in a diagram.

- The answer is 70.
- We must also add 70 because degrees are the same size on both scales.

- To convert from Celsius to theKelvin scale, we have to add the temperature in Cdeg to 273.

- The picture to the left shows the two temperature scales.
- That is, 77 K is less than 273 K.

- We want to solve for the Celsius temperature.
- We want to keep the equals sign out of the way.
- The same thing is done on both sides of the equals sign to preserve equality.
- It's always a good idea to do the same operation on both sides of the equals sign.

- There are two problems, Problems 2.73 and 2.74.

- The National Institute for Materials Science in Tsukuba, Japan, produced the device.
- A powerful electron microscope is needed to read the tiny thermometer.

- The tiny thermometers were made by mistake.
- The Japanese scientists were trying to make tiny wires.
- When they looked at the results of their experiment, they found tiny tubes of carbon atoms that were filled with gallium.
- gallium makes a perfect working liquid because of its large temperature range.
- Mercury thermometers have mostly been phased out because of the toxicity of mercury, but the gallium expands as the temperature increases.
- As the temperature increases, gallium moves up the tube.

- There is a change in the level of liquid gallium within a carbon nanotubes.

- The minuscule thermometers can't be seen with the naked eye.

- Because the scales have the same size unit, we must account for the different zero points to switch from one scale to the other.

- The diagram in Figure 2.9 shows how to adjust for different unit sizes.

- It's okay to do the same thing to both sides of the equation.

- The factor is used to convert from one degree size to another.

- The difference in degree size between the scales is taken into account in this equation.
- We will show you how to use it.

- This is an interesting result and a useful reference point.

- Hot tub maintenance is done at 41.
- Cdeg.

- Problems 2.75, 2.76 and 2.77 can be found here.

- To convert a temperature to a degree, we need to rearrange the equation.
- We can always do the same thing to both sides of the equation.

- The body's response to an injury is to raise its temperature.

- Problems 2.75, 2.76 and 2.77 can be found here.

- The following formulas are used for temperature conversions.

- Density and its units are defined.

- If you said lead, you were thinking about density.
- Density is the amount of matter present in a given volume of substance.

- It takes a lot more to make a pound of feathers than it does to make a pound of lead.
- Lead has a denser mass per unit volume.

- The density of a liquid can be determined by weighing a known volume of the substance.

- A student might find that a certain liquid has a weight of 35.062 g.

- Submerging a solid object in water and measuring the volume of water displaced is how the volume of a solid object is determined.
- This is the most accurate method for measuring a person's percent body fat.
- The increase in volume is measured when a person is submerged in a tank of water.
- The person's weight and volume can be used to calculate the body density.
- The fraction of the person's body that is fat can be calculated because of the different densities of fat, muscle, and bone.
- The density of a person's body is determined by the amount of muscle and fat he or she has.
- A fat person with a body volume of 150 lbs has a higher density than a muscular person with a body volume of 150 lbs.

- At a pawn shop, a student finds a piece of jewelry that the owner insists is pure Platinum.
- The student thinks the medallions may be silver and less valuable.
- If the shop owner agrees to refunds the price, the student buys the medallions.
- The student takes the medallion to her lab to measure its density.
- She weighed the medallions and found its mass to be 55.64 g. She places some water in a graduated cylinder and reads the volume.
- She drops the medallion into the cylinder and reads the new volume.

- The measured density of the medallion will show which metal is present.

- 55.64 g is the mass of the medallion.
- If you take the difference between the volume readings of the water in the graduated cylinder before and after the medallion is added, you can get the volume.

- When the medallion was added, the volume appeared to increase by 2.6 mL.

- The gold is really shiny.

- A student is looking at a commercial liquid cleaner.

- Problems 2.89 and 2.90 can be seen.

- The density of Mercury is 13.6 g/mL.

- We want to find the volume.
- When we do the same thing to both sides, we maintain an equality.

- To get the amount that has a mass of 225 g, we have to take a large amount of mercury.

- The densities of various substances are given in Table.
- Density is a tool for the identification of substances.
- The density of the liquid in your car's lead storage battery can be changed by the amount of sulfuric acid consumed as the battery discharges.
- Density measurement is used to determine the level of protection against freezing in the cooling system of a car.
- The density of the mixture tells us how much of each is present.
- Figure 2.11 shows the device used to test the density of the solution.

- Mercury is pouring from a pipette.

- A hydrometer is being used to determine the density of the solution in the car's engine.

- Specific gravity is used to describe the density of a liquid.
- Specific gravity has no units because it is a ratio of densities.

- A measurement consists of a number and a unit.
- The number is expressed as a number between 1 and 10 and raised to a power.
- The scale on which to represent the results of a measurement is provided by units.
- There are three commonly used unit systems, EnglishMetric,SI, which use prefixes to change the size of the unit.
- There are rules for rounding off the correct number of figures.
- We can use conversion factors to convert from one system of units to another.
- The zero point and the size of the unit can be adjusted to convert among the scales.

- Group of students in class will be asked these questions.
- For introducing a topic in class, these questions work well.

- The Student Solutions Guide has full solutions for the questions and problems below.

- A quantitative observation is represented by 1.A.

- Students remember the rules for converting an ordinary number to scientific notation better if they put them into their own words.
- Pretend you are helping your niece with her math homework, and write a paragraph explaining to her how to convert the ordinary number 2421 to scientific notation.
- The order of magnitude of the number needs to be expressed as a power of 10 in order to be considered scientific.
- To move the decimal point three places to the left in going from 2421 to 2.421 requires a power of 103 after the number.
- When a large or small number is written in standard scientific notation, the number is expressed as the product of the number between 1 and 10.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The English system has made it difficult for students to relate the metric system to it.
- The approximate English system equivalents for each of the following metric system descriptions are given.

- 25 square meters of linoleum is required for my new kitchen floor.
- The gas tank in my new car holds 48 liters.

I just passed a road sign that said "New York City 100 km."

- The gps in my car shows that I have 100.

- The tablecloth on my dining room table is 2 m long.

- Who is taller, a man who is 1.62 m tall or a woman who is 5 ft6 in.
- We often deal with larger or smaller distances for which multiples or fractions of the fundamental unit are more useful.
- The size of your bedroom, the thickness of your hair, and the distance between Chicago and Saint Louis are all examples of situations where a fraction or multiple of the meter might be the most appropriate measurement.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The last significant digit recorded for the measurement is said to be uncertain, when a measuring scale is used to the limit of precision.

- You report a volume of water in the lab.

- Explain why the pin's length is stated as 2.85 cm rather than the previous figure's length of 2.83 cm.
- The scale was marked to the nearest hundredth of a centimeter, and that the zero in the thousandths place had been estimated.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The Student Solutions Guide has full solutions for the questions and problems below.

- If the number to the right of the digit is greater than 5, then we should round it off.

- To carry through extra digits in intermediate calculations is better to round off only the final answer.
- rounding off in each step may cause a cumulative error in the final answer.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The answer to this calculation should be reported to only two significant digits.
- The water was measured with a beaker, graduated cylinder, and buret.
- Support your answer.
- You don't need to do the calculation.
- To determine the perimeter of the cover of your textbook, you are asked.
- The length is 34.29 cm and the width is 26.72 cm.
- You don't need to do the calculation.

- See the Appendix for help in doing mathematical operations with numbers.

- The answer to the correct number of significant digits can be found in the following mathematical expressions.
- Do not do the calculations.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The ratio is based on an equivalence statement.

- The price for apples is $1.75 per pound.

- The back cover of the book contains appropriate equivalence statements for various units.

- Setting up the appropriate conversion factor in each case is required to perform each of the following conversions.
- Los Angeles and Honolulu are 2558 miles apart.
- The United States has high-speed trains between Boston and New York that can go up to 160 miles per hour.

- The Student Solutions Guide has full solutions for the questions and problems below.

- The temperature scale is used in most of the world except the United States.
- The freezing/melting point of water is at 32 degrees.
- The normal boiling point of water is Fdeg.
- The normal freezing point of water is 273 K.

- The Student Solutions Guide has full solutions for the questions and problems below.

- g/ cm3 is the most common unit for density.
- A kilogram of lead has a higher density than a kilogram of water.

- Density is a characteristic property of a pure substance.

- You don't have to evaluate the expression if you know the number of significant digits in the answer.
- Explain your reasoning and account for all five zeros in the measurement.
- What is the average height of the Xgnuese?
- What is the height in blims?
- The book's cover is 72.5 square.

- A man who is 1.52 m tall is taller than a woman who is 5 ft3 in.

- Suppose your car is rated at 45 miles per gallon for highway use and 38 miles per gallon for city driving.
- You want to buy some fruit for lunch in Paris.
- There is a sign in the fruit stand that shows the price of peaches.
- It is easier for a pharmacy to weigh the medication than it is to count the individual pills.
- The natives have 14 fingers.
- A gas cylinder has a volume of 10 L.

- When 2891 is written in scientific notation, the power of 10 is shown.

In each case, will the exponent be positive, negative, or zero?

- The metric system has a fundamental unit of length or distance.

- The student's answer depends on the glassware used.

- The distance is also expressed as 0.105 m.

- Which weighs more, 1 g of water or 1 g of water?
- They both weigh the same.

- The 500 m length can be expressed as 10x1011.

- The same type of assistance a student would get from an instructor can be found in these multiconcept problems.

- The following table shows the number of significant figures for each mathematical expression.

- The longest river in the world is the Nile River.
- The melting point of phosphorus is 44.
- The density of osmium is 22.57 and is the densest metal.
- ]g/ cm3.

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