TUTORIAL SHEET 2 - ACCURACY , PRECISION, UNCERTAINTIES AND CONVERSION OF UNITS
1. The sides of a small rectangular box are measured to be 1.80 ± 0.01 cm , 2.05 ± 0.02 cm, and 3.1
± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.
2. The distance moved by an object is 4 ± 0.1 m and the time taken is 2 ± 0.2 s. Find the average
speed and the uncertainity in the average speed.
3. A rectangular plate has a length of (21.3 ± 0.2) cm and a width of (9.8±0.1) cm. Calculate the
area of the plate, including its uncertainty.
4. The radius of a solid sphere is measured to be (6.50 ± 0.20) cm, and its mass is measured to be
(1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the
uncertainty in the density.
5. A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its
percent uncertainty?
6. The length and width of a rectangular room are measured to be 3.955 ± 0.005 m and 3.050 ±
0.005 m . Calculate the area of the room and its uncertainty in square meters.
7. Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the
uncertainty in your mass (in kilograms)?
8. A solid piece of copper wire has a mass of 23.94 kg and volume 2.10 cm3. Calculate the density
of the copper wire in SI units (
/ mm3).
9. The volume of a wallet is 8.50 in.3 Convert this value to m3, using the definition 1 in. = 2.54 cm.
10. A worker is to paint the walls of a square room 8.00 ft high and 12.0 ft along each side. What
surface area in square meters must she cover?
11. Suppose your hair grows at the rate of 1/32 in. per day. Find the rate at which it grows in
meters per second.
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