Unit conversion and significant figures: rules + examples

Key ideas

Conversion factors

A conversion factor is a fraction whose top and bottom are the same amount, so multiplying by it does not change the value. Put the unit you want to cancel on the bottom:

5.0\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} = 5000\ \text{m}

Common conversions (the first four are exact by definition)
Conversion	Factor
inch to centimeter	1 in = 2.54 cm
mile to meter	1 mi = 1609.344 m
hour to second	1 h = 3600 s
kilo, centi, milli	1 km = 1000 m, 1 m = 100 cm, 1 m = 1000 mm
liter to cubic centimeter	1 L = 1000 cm³ = 1000 mL
km/h to m/s	divide by 3.6

Counting significant figures

Nonzero digits always count: 4.56 has 3.
Zeros between nonzero digits count: 1.005 has 4.
Leading zeros never count: 0.0032 has 2.
Trailing zeros count only if there is a decimal point: 2.500 has 4, but 2500 has 2. Write $2.50 \times 10^3$ to show 3.
Exact numbers, like counted objects or defined conversions (1 in = 2.54 cm), have unlimited significant figures.

Rounding answers

Multiply or divide: keep the fewest significant figures of any measurement. $4.56 \times 1.4 = 6.384$ , which rounds to 6.4 (2 significant figures).
Add or subtract: keep the fewest decimal places. $12.11 + 18.0 + 1.013 = 31.123$ , which rounds to 31.1 (1 decimal place).
Keep extra digits during a long calculation, and round only once at the end.

Worked examples

Example 1: miles per hour to meters per second

Problem A car drives at 65 mph. What is that in m/s?

Chain two factors: miles to meters, then hours to seconds.
$65\ \frac{\text{mi}}{\text{h}} \times \frac{1609.344\ \text{m}}{1\ \text{mi}} \times \frac{1\ \text{h}}{3600\ \text{s}} = 29.06\ \text{m/s}$
The conversion factors are exact, so the 2 significant figures of 65 decide the answer.

Answer 29 m/s

Example 2: converting a unit that is squared or cubed

Problem Convert a density of 2.5 g/cm³ to kg/m³.

Grams to kilograms: divide by 1000. Cubic centimeters to cubic meters: 1 m = 100 cm, so 1 m³ = $100^3 = 10^6$ cm³.
$2.5\ \frac{\text{g}}{\text{cm}^3} \times \frac{1\ \text{kg}}{1000\ \text{g}} \times \frac{10^6\ \text{cm}^3}{1\ \text{m}^3} = 2500\ \text{kg/m}^3$
Show 2 significant figures with scientific notation.

Answer $2.5 \times 10^3$ kg/m³

Example 3: counting significant figures

Problem How many significant figures are in 0.004050?

The leading zeros (0.00) only place the decimal point. They do not count.
4 and 5 count, the zero between them counts, and the trailing zero counts because there is a decimal point.

Answer 4 significant figures

Example 4: a mixed calculation

Problem A runner covers 100.0 m, then 52.5 m, in a total time of 21.6 s. What is the average speed?

Add first. Both distances have 1 decimal place, so the sum keeps 1.
$100.0 + 52.5 = 152.5\ \text{m}$
Then divide. 152.5 has 4 significant figures and 21.6 has 3, so the answer gets 3.
$\frac{152.5\ \text{m}}{21.6\ \text{s}} = 7.060\ \text{m/s}$

Answer 7.06 m/s

Common mistakes and how to fix them

Flipping the conversion factor. Fix: write the units on every number. If the unit does not cancel, turn the fraction over.
Converting squared units with the plain factor. 1 m² is 10,000 cm², not 100. Fix: square or cube the factor too.
Using the sig fig rule for multiplication when adding. Fix: addition and subtraction go by decimal places.
Rounding in the middle. Fix: keep one or two extra digits until the final answer.
Counting the digits of an exact number. "3 trials" or "1 h = 60 min" never limit your answer.

Practice problems

How many significant figures are in 0.00320?
1. 2
2. 3
3. 5
4. 6
Show answer
Answer: 3
The leading zeros do not count. 3 and 2 count, and the final zero counts because there is a decimal point.
How many significant figures are in 1500 (no decimal point)?
1. 2
2. 3
3. 4
Show answer
Answer: 2
Trailing zeros without a decimal point are not significant. To show 4, write 1500. or $1.500 \times 10^3$ .
Convert 72 km/h to m/s.
Show answer
Answer: 20. m/s
$72 \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{h}}{3600\ \text{s}} = 20.$ m/s. The decimal point shows that both digits are significant.
Calculate $3.0 \times 2.26$ with the correct significant figures.
1. 6.78
2. 6.8
3. 7
4. 6.780
Show answer
Answer: 6.8
$3.0 \times 2.26 = 6.78$ . 3.0 has only 2 significant figures, so round to 6.8.
A pencil is 5.00 inches long. How long is it in centimeters?
Show answer
Answer: 12.7 cm
$5.00\ \text{in} \times 2.54\ \text{cm/in} = 12.7$ cm. 2.54 is exact, so 5.00 sets 3 significant figures.

Frequently asked questions

Why do significant figures matter?

They show how precise a measurement is. If a ruler measures to the nearest millimeter, writing a length to a millionth of a meter claims precision you do not have. Answers keep the precision of the least precise measurement, so they never look more exact than the data.

Do I round 2.5 up or down?

Most high school classes round 5 up, so 2.5 becomes 3. Some science courses and computers round a 5 to the nearest even digit instead, so 2.5 becomes 2. Follow your teacher's rule. It rarely matters, because you should keep extra digits until the end anyway.

What is dimensional analysis?

It is another name for converting with conversion factors and checking that units cancel. It also catches mistakes: if a speed problem ends in seconds per meter instead of meters per second, a step is upside down. Chemistry uses the same method for moles and molar mass.

Sources

OpenStax College Physics 2e, 1.2 Physical Quantities and Units, accessed October 1, 2026
OpenStax College Physics 2e, 1.3 Accuracy, Precision, and Significant Figures, accessed October 1, 2026
NIST, Guide for the Use of the SI (Appendix B conversion factors), accessed October 1, 2026