Practice Measurement in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Measurement is the process of assigning numerical values to attributes of objects or events according to a defined rule or scale.

To measure is to quantify—turning 'how much' or 'how many' into a number.

Showing a random 20 of 50 problems.

Example 1

hard
A reaction time test is repeated 9 times by one student, giving SD =0.06= 0.06 s. What is the standard error of the mean of these 9 trials?

Example 2

challenge
A cube's side is measured as 2.02.0 cm with ±0.1\pm0.1 cm uncertainty. Roughly, is the relative uncertainty in the side 5%5\%, and why does volume amplify it?

Example 3

easy
A pitcher holds 2.52.5 liters of water. How many milliliters is this?

Example 4

medium
A track meet timer is consistently 0.30.3 s slow because of a calibration drift. Is this random or systematic error, and does averaging many race times remove it?

Example 5

easy
Convert 250250 centimeters to meters.

Example 6

medium
Why must units accompany a measured value like '5'?

Example 7

easy
A scale displays a child's mass as 25.025.0 kg with ±0.1\pm 0.1 kg uncertainty. Give the range of plausible true masses.

Example 8

medium
A jug has 2.02.0 L of water; you pour out 750750 mL. How much remains, in liters?

Example 9

easy
To measure how heavy an object is, which attribute and unit are appropriate?

Example 10

easy
Is a measured value ever perfectly exact?

Example 11

medium
A lab averages 10 repeated mass readings to report a single value. What measurement benefit does averaging provide?

Example 12

medium
A student adds 2020 cm and 0.150.15 m and reports 20.1520.15. What unit error did they make, and what is the correct sum in meters?

Example 13

hard
A protractor reads angles to the nearest 1°. You measure an angle as 48°48°. What is the range of true angles, and what is the relative uncertainty?

Example 14

medium
Three students measure a table's length: 120.1,120.0,119.9120.1, 120.0, 119.9 cm. The true length is 120.0120.0 cm. Describe the measurements' precision and accuracy.

Example 15

medium
Add 1.51.5 m and 3030 cm, giving the result in meters.

Example 16

easy
A measurement is recorded as 12.012.0 cm with the note 'plus or minus 0.10.1 cm.' What does the ±0.1\pm0.1 represent?

Example 17

easy
A scale reads 3.03.0 kg, 3.13.1 kg, 2.92.9 kg for the same object. The true mass is 5.05.0 kg. Is the scale precise or accurate?

Example 18

easy
Convert 15001500 grams to kilograms.

Example 19

hard
A thermometer reads the boiling point of water as 99.2°C at sea level (true value: 100°C). If 10 repeated readings give mean 99.2°C with SD=0.3°C, identify the type(s) of error and suggest how to address each.

Example 20

medium
A speedometer is checked against GPS five times, reading consistently 22 mph below the true speed each time. Is the issue random or systematic?