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1.4 Approximation

- The input quantities are only known to a limited degree.
- As you develop problem-solving skills that can be applied to a variety of fields through a study of physics, you will also develop skills at approximating.
- You will be able to develop these skills if you are willing to take risks.
- We can rule out certain scenarios with these approximations.
- Approximations allow us to challenge others and guide us in our approaches to science.
- Let's do two examples to show this concept.

- We can make an approximation based on height.
- We will calculate the height of the building.

- Think about the height of an adult male.
- The height of the building can be approximated by scaling up from the height of a person.

- We know that there are 39 stories in the building.

- An approximate measurement of unknown quantities can be determined using known quantities.

- A stack of 100 bills is worth $10,000.
- Most of us don't know how much one trillion is.
- If you were given a trillion dollars in $100 bills, what would you do with it?
- Make an approximation of how high the money pile would become if you made 100 bill stacks and used them to evenly cover a football field.

- When you think of a situation like this, you think of thousands of small stacks of 100 wrapped $100 bills, like you would see in movies or at a bank.
- Let's start there since this is an easy-to-approximate quantity.
- We can find the volume of a stack of 100 bills, find out how many stacks make up one trillion dollars, and then set this volume equal to the area of the football field.

- The bill's dimensions are 3 in.
- There is a stack of 100 of these.

- Determine the number of stacks.

- The area of a football field is calculated in square inches.

- The area of the field is given by this conversion.

- The height is calculated using the volume of the -bill stacks.

- The money will be about 100 in.

- Mental math and understanding of fundamental units can be used to approximate the area of a basketball court.

- The average male is about two meters tall.
- It would take 15 men to cover the length and 7 to cover the width.

- Science seeks to discover and describe the underlying physical quantities and units.

- The general truths expressed in combinations of four fundamental units are scientific laws and theories.

- All natural processes the meter for length and the kilogram for mass according to these laws of nature.

- The metric system uses powers of 10 to relate quantities over the vast ranges encountered in nature.

- The four fundamental units are abbreviated as follows.

- The precision of a measuring tool is related to the size of the metric system.
- The smaller the order of magnitude, the more precise the tool is.

- Significant figures are used to express the precision of a measuring.

- Conversion factors, which are ratios relating equal final answer can only contain as many significant quantities as measured values.

- The final Significant Figures answer cannot contain more than the least precise value.

- The accuracy of a measurement is related to how close a measurement is to the correct value.
- Uncertainty in a measurement is an estimate of the amount by which scientists approximate the values of quantities to the measurement result.

- There are models that are useful in both quantum and relativity.

- Mention some advantages of metric units.

- For an expected result, prescriptions for vision correction are the same as for an unexpected diopters.
- Determine the meaning of that unit.

- Classical physics is an approximation to modern physics.

When is it necessary to use quantum mechanics?

- American football is played on a long field.

- Soccer fields can be large or small.

- The car is moving fast.

- What is the height in meters of a person who is 6 ft 1.0 in.

- A blood pressure measurement on a certain day can affect the speed of sound.

- A person measures his or her heart rate by counting slowly.
- A plate with a number of beats in it.
- If beats are counted in the average speed.

How long does a marathon run between the Earth and the Sun?

- A runner completes a course.

- There is an uncertainty of 1.3 Accuracy, Precision, and in the distance traveled and an uncertainty of 1 s in the Significant Figures elapsed time.

- The sides of a small box have a 3% uncertainty.

- A good-quality measuring tape can be off by 0.50 cm.

How many beats does he or she have?

- There is a can of soda.

How many important figures are there to compress the gas in the cylinder?

- A generation is 1/3 of a lifetime.

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