1.2.3 Uncertainty in Measurement and Significant Digits

Question 1

Uncertainty in Measurement and Significant Digits

Answer 1

• When measuring a quantity, the convention is that the last number is the last digit you can believe. This number is called the last significant digit or significant figure.
• Given a number, its trailing zeros are significant digits, while its leading zeros are not, these are just placeholders.
• When multiplying, dividing, adding or subtracting, the final answer should have the same number of significant digits as the least accurate quantity.

Question 2

note

Answer 2

• A significant digit is a reliably known figure, other than the zeros to locate the decimal point.
• Trailing zeros are significant zeros, while leading zeros are not, these are just placeholders.
• Suppose the measurement of the length of an object is: L=200 m.
• Question: Are the zeros trailing or not?
• Answer: It depends on the accuracy of the measuring device.
• If the measurement is just an approximation, the length should be reported as: If the measurement is accurate to three significant digits, it should be reported as:
• When multiplying, dividing, adding or subtracting, the final answer should have the same number of significant digits as the least accurate quantity.
• It is acceptable to include many digits in the intermediate calculations, but remember than the final answer cannot have more significant digits than the least accurate quantity

Question 3

Suppose that an environmental study determines that a town produces approximately 2,000 lb of trash each day. The study group decides to convert their findings to SI units, using the conversion 1 lb = 0.4536 kg. They report that the town produces 907.2 kg of trash each day. Which of the following is correct?

Answer 3

The study group used the correct conversion factor but did not account for significant digits.

Question 4

Which of the following shows a measurement that has precisely two significant figures?

Answer 4

98 m

Question 5

Suppose you are asked to determine the perimeter of a seven-sided irregular figure. You make the following measurements:
Side 1 = 3.2 m
Side 2 = 4.8 m
Side 3 = 2.000 m
Side 4 = 8.94 m
Side 5 = 11 m
Side 6 = 7.566 m
Side 7 = 4.0 m
How many significant figures should there be in your calculation for the perimeter?

Answer 5

two significant figures

Question 6

How many significant figures are there in a measurement 0.30700 cm?

Answer 6

Five significant figures — every digit except the first 0.

Question 7

Which of the following statements concerning significant figures is not correct?

Answer 7

Not all of physics is verifiable.

Question 8

The circumference of a circle is 2(pi)(r). Suppose that r = 0.0347. Which of the following correctly shows the circumference of the circle?

Answer 8

C = 0.218 m

Question 9

Suppose you have $100 that you need to convert to Danish kroner. The conversion rate that day is 5.732 Danish kroner for one American dollar. The business that converts your money charges you a flat fee of 50 Danish kroner for the transaction.

Use your knowledge of significant figures to decide which of the following shows the correct amount of Danish kroner that you should receive.

Answer 9

523.2 Danish kroner

Question 10

Suppose you are told that the mass of an object is 1.283 kg. What is the implied range for the mass of this object?

Answer 10

1.282 kg –> 1.284 kg

Question 11

How many sig-figs should there be for the product of 29 * 3.530m?

Answer 11

two significant figures