2.1: Units and Measurements

• Metric System: A system of measurement used by scientists and in most countries of the world.

• International System of Units (SI): Also known as Système International; the official system of measurement throughout the world except for the United States.

Units of Measurement and their Abbreviations

Length

• The metric and SI unit of length is the meter (m).

• A meter is 39.4 inches, which makes it slightly longer than a yard.

• A centimeter (cm) is a smaller unit of length and is commonly used in chemistry.

Volume

• Volume: The amount of space a substance occupies.

• The metric and SI unit of volume is the liter (L).

• Millimeter (mL) is a smaller and more convenient unit of volume, mostly used by chemists at laboratories or hospitals.

Mass

• Mass: The measure of the quantity of material it contains.

• The SI unit of mass, the kilogram (kg) — used for larger masses.

• Gram (g) is used for smaller masses.

• Weight: The measure of the gravitational pull on an object.

Temperature

• Temperature tells us how hot something is, how cold it is outside, or helps us determine if we have a fever.

• In the metric system, temperature is measured using Celsius temperature.

  • On the Celsius (°C) temperature scale, water freezes at 0 °C and boils at 100 °C.

  • On the Fahrenheit (°F) temperature scale, water freezes at 32 °F and boils at 212 °F.

• In the SI system, the temperature is measured using the Kelvin (K) temperature scale, on which the lowest possible temperature is 0 K.

Time

• We typically measure time in units such as years (yr), days, hours (h), minutes (min), or seconds (s).

• Of these, the SI and metric unit of time is the second (s).

• The standard now used to determine a second is an atomic clock.

2.2: Measured Numbers and Significant Figures

• Measured numbers: The numbers you obtain when you measure a quantity such as your height, weight, or temperature.

• Significant figures (SFs): All the digits including the estimated digit. Nonzero numbers are always counted as significant figures.

• Exact Numbers: Those numbers are obtained by counting items or using a definition that compares two units in the same measuring system.

  • These are not measured, do not have a limited number of significant figures, and do not affect the number of significant figures in a calculated answer.

• Zeros in front of a decimal number or at the end of a nondecimal number are not significant.

2.3: Significant Figures in Calculations

Rounding Off

• If the first digit to be dropped is 4 or less, then it and all the following digits are simply dropped from the number.

• If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.

Multiplication and Division with Measured Numbers

• In multiplication or division, the final answer is written so that it has the same number of significant figures as the measurement with the fewest SFs.

Adding Significant Zeroes

• Sometimes, a calculator display gives a small whole number.

• Then we add one or more significant zeros to the calculator display to obtain the correct number of significant figures.

Addition and Subtraction with Measured Numbers

• In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.

2.4: Prefixes and Equalities

• The special feature of the SI as well as the metric system is that a prefix can be placed in front of any unit to increase or decrease its size by some factor of 10.

• Prefixes such as centi, milli, and micro provide smaller units; prefixes such as kilo, mega, and tera provide larger units

Metric and SI Prefixes

Measuring Length

• When the prefix centi- is used with the unit meter, it becomes centimeter, a length that is one-hundredth of a meter (0.01 m).

• When the prefix milli- is used with the unit meter, it becomes a millimeter, a length that is one-thousandth of a meter (0.001 m).

• Equalities: This shows the relationship between two units that measure the same quantity.

Measuring Volume

• When a liter is divided into 10 equal portions, each portion is a deciliter (dL).

• There are 10 dL in 1 L.

• Laboratory results for blood work are often reported in mass per deciliter.

• When a liter is divided into a thousand parts, each of the smaller volumes is called a milliliter (mL).

• Cubic centimeter: The volume of a cube whose dimensions are 1 cm on each side. It has the same volume as a milliliter, and the units are often used interchangeably.

Measuring Mass

• A kilogram is equal to 1000 g.

• One gram represents the same mass as 1000 mg, and one mg equals 1000 μg.

• When you go to the doctor for a physical examination, your mass is recorded in kilograms, whereas the results of your laboratory tests are reported in grams, milligrams, or micrograms.

2.5: Writing Conversion Factors

• Conversion Factors: Any equality that can be written as fractions; with one of the quantities in the numerator and the other quantity in the denominator.

• The numbers in any equality between two metric units or between two U.S. system units are obtained by definition.

• When equality consists of a metric unit and a U.S. unit, one of the numbers in the equality is obtained by measurement and counts toward the significant figures in the answer.

• The usefulness of conversion factors is enhanced by the fact that we can turn a conversion factor over and use its inverse.

• An equality may also be stated within a problem that applies only to that problem.

• Equalities stated within dosage problems for medications can also be written as conversion factors.

• A percentage is written as a conversion factor by choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole.

2.6: Problems Solving Using Unit Conversion

• The process of problem-solving in chemistry often requires one or more conversion factors to change a given unit to the needed unit.

• Conversion factors are useful when changing a quantity expressed in one unit to a quantity expressed in another unit.

• In the problem-solving process, a given unit is multiplied by one or more conversion factors that cancel units until the needed answer is obtained.

2.7: Density

• Density: The mass and volume of any object can be measured.

• If we compare the mass of the object to its volume, we obtain density.

• The volume of a solid can be determined by volume displacement.

  • When a solid is completely submerged in water, it displaces a volume that is equal to the volume of the solid.

• Density can be used as a conversion factor.

  • If the volume and the density of a sample are known, the mass in grams of the sample can be calculated.

• Specific Gravity: A relationship between the density of a substance and the density of water.

• Hydrometer: An instrument often used to measure the specific gravity of fluids.

Problem Solving with Density

John took 2.0 teaspoons 1tsp2 of cough syrup for a persistent cough. If the syrup had a density of 1.20 g>mL and there is 5.0 mL in 1 tsp, what was the mass, in grams, of the cough syrup?

• Step 1: State the given and needed quantities.

• Step 2: Write a plan to calculate the needed quantity.

• Step 3: Write the equalities and their conversion factors including density.

• Step 4: Set up the problem to calculate the needed quantity.

• Answer: The density of maple syrup is 1.33 g>mL. A bottle of maple syrup contains 740 mL of syrup.

Problem Solving with Specific Gravity

You have a sample of granite with density 174.8 lbs/ft3. The density of water is 62.4 lbs/ft3. What is the specific gravity of the granite now?