A significant figure is a digit that carries information about size. Choosing a sensible number of them means your final answer should not look more precise than the data you started with. This appears whenever a question says “give your answer to 3 significant figures” and whenever you must decide for yourself.
It is the first lesson in precision bounds and measurement because every later lesson depends on knowing what a rounded value really means.
Which digits are significant?
Count from the first non-zero digit. Zeros at the start are placeholders, not information.
| Number | Significant figures | Why |
|---|---|---|
| 0.00702 | 3 | The zeros at the start do not count; 7, 0, 2 do |
| 0.0700 | 3 | 7, then the two zeros after the decimal point |
| 40.05 | 4 | The zero between 4 and 5 counts |
| 7020 | 3 or 4 | The last zero may be a placeholder, so the question’s wording decides |
How do you round to a given number of significant figures?
- Find the first significant digit and count across to the last digit you will keep.
- Look at the next digit. If it is 5 or more, round the last kept digit up. Otherwise leave it.
- Keep the size. Fill any gap with zeros so that 38 649 to 2 sf becomes 39 000, not 39.
For example, 0.0072846 to 3 sf keeps 7, 2, 8 and the next digit is 4, so the answer is 0.00728.
Also, 5.996 to 3 sf rounds up to 6.00. The zeros in 6.00 stay on purpose because they show three significant figures.
Worked example
A runner covers 845 m in 62 s. Find the average speed in m/s, giving a sensible accuracy.
Step 1, divide: 845 ÷ 62 = 13.629…
Step 2, compare the data: 845 has three significant figures and 62 has two. The weaker value limits the result.
Step 3, round to match the weaker value: 13.629… to 2 sf is 14 m/s.
Writing 13.629 m/s would suggest the time was measured to the nearest thousandth of a second, which the question never said.
The mistake to watch for
A common slip is rounding in the middle of a calculation.
Mistaken working: 18 ÷ 7 = 2.6 (rounded), then 2.6 × 35 = 91.
The student rounded too early, so the error was multiplied by 35.
The correct approach keeps the exact value: 18 ÷ 7 × 35 = 90, because 35 ÷ 7 = 5 and 5 × 18 = 90. Rounding early gave 91, which is wrong in the second significant figure.
Use the calculator’s memory or write 18/7 as a fraction, and round only when you write the final line.
Check yourself
Try these, then open each answer.
1. Write 0.0050382 to 3 significant figures.
Show answer
The significant digits start at 5: 5, 0, 3 are the first three. The next digit is 8, so round the 3 up to 4. The answer is 0.00504.
2. Write 6972 to 2 significant figures.
Show answer
The first two digits are 6 and 9. The next digit is 7, so 69 rounds up to 70. Keep the size: 7000.
3. How many significant figures does 0.0450 have?
Show answer
The zeros at the start do not count. The digits 4, 5 and the final 0 count, so there are 3 significant figures.
Where this leads next
Next, see how a rounded number hides a whole range of possible values in recover an interval from a rounded measurement. The non-calculator working trainer helps you practise exact steps before you round.
Some students round correctly but still lose marks because they choose the wrong accuracy or round too soon. A teacher in online one-to-one Mathematics tuition can trace that pattern through your written working.