1.3 Accuracy, Precision, and Significant Figures

A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05 s. The team's top sprinter clocked a 100 meter sprint at 12.04 seconds last week and at 11.96 seconds this week. Can we conclude that this week's time was faster?

Determine the number of significant figures in the following measurements:

1. 0.0009
2. 15,450.0
3. $6 \times \text{10}^{3}$
4. 87.990
5. 30.42

Perform the following calculations and express your answer using the correct number of significant digits.

(a) A woman has three bags: two of the bags weigh 13.5 pounds each, and one bag weighs of 10.2 pounds. What is the total weight of the bags?

(b) The force $F$ on an object is equal to its mass $m$ multiplied by its acceleration $a$. If a wagon with mass 55 kg accelerates at a rate of $0.0255 \text{ m}/\text{s}^{2}$, what is the…

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

Express your answers to problems in this section to the correct number of significant figures and proper units.

(a) A car speedometer has a $5.0 \%$ uncertainty. What is the range of possible speeds when it reads $\text{90} \text{km}/\text{h}$? (b) Convert this range to miles per hour. $\left(\text{1 km} = \text{0}.\text{6214 mi}\right)$

Express your answers to problems in this section to the correct number of significant figures and proper units.

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats do they have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

Express your answers to problems in this section to the correct number of significant figures and proper units.

State how many significant figures are proper in the results of the following calculations: (a) $\left(\text{106} . 7\right) \left(\text{98} . 2\right) / \left(\text{46} . \text{210}\right) \left(1 . \text{01}\right)$ (b) $\left(\text{18} . 7\right)^{2}$ (c) $\left(1 . \text{60} \times \text{10}^{- \text{19}}\right) \left(\text{3712}\right)$.

Express your answers to problems in this section to the correct number of significant figures and proper units.

(a) If your speedometer has an uncertainty of $2 . 0 \text{km}/\text{h}$ at a speed of $\text{90} \text{km}/\text{h}$, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads $\text{60} \text{ km}/\text{h}$, what is the range of speeds you could be going?

Express your answers to problems in this section to the correct number of significant figures and proper units.

A person measures their heart rate by counting the number of beats in $\text{30} \text{s}$. If $\text{40} \pm 1$ beats are counted in $\text{30} . 0 \pm 0 . 5 \text{s}$, what is the heart rate and its uncertainty in beats per minute?

Express your answers to problems in this section to the correct number of significant figures and proper units.

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

Express your answers to problems in this section to the correct number of significant figures and proper units.

The sides of a small rectangular box are measured to be $1.80 \pm 0.01 \text{cm}$, $$$2.05 \pm 0.02 \text{cm},\text{ and 3}.\text{1} \pm 0.1 \text{cm}$ long. Calculate its volume and uncertainty in cubic centimeters.

Express your answers to problems in this section to the correct number of significant figures and proper units.

The length and width of a rectangular room are measured to be $3 . \text{955} \pm 0 . \text{005} \text{m}$ and $3 . \text{050} \pm 0 . \text{005} \text{ m}$. Calculate the area of the room and its uncertainty in square meters.