0.6 Accuracy, precision, and significant figures  (Page 5/11)

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

(a) A woman has two bags weighing 13.5 pounds and one bag with a weight 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 $0\text{.}\text{0255 }{\text{m/s}}^2$ , what is the force on the wagon? (The unit of force is called the newton, and it is expressed with the symbol N.)

What is the relationship between the accuracy and uncertainty of a measurement?

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

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a $5.0\text{\%}$ uncertainty. What is the range of possible speeds when it reads $\text{90}\text{km/h}$ ? (b) Convert this range to miles per hour. $\left(\text{1 km}=\text{0.6214 mi}\right)$

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

A can contains 375 mL of soda. How much is left after 308 mL is removed?

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

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

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

What is the area of a circle $3\text{.}\text{102}\text{cm}$ in diameter?

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

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where $1\text{lbm}=0\text{.}\text{4539}\text{kg}$ . (a) If there is an uncertainty of $0\text{.}\text{0001}\text{kg}$ in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

A car engine moves a piston with a circular cross section of $7\text{.}\text{500}\pm 0\text{.}\text{002}\text{cm}$ diameter a distance of $3\text{.}\text{250}\pm 0\text{.}\text{001}\text{cm}$ to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.