The first significant figure of a number is its first non-zero digit, reading from the left. To round to a number of significant figures, count from that digit and apply the usual rule: look at the next digit and round up if it is 5 or more. Fill with zeros to keep large numbers the right size. Truncation is different: it simply chops off the extra digits without rounding.
Significant figures and truncation
- First significant figure: the first non-zero digit from the left
- Leading zeros (0.00…) are not significant; zeros between digits are
- Round: look at the next digit, 5 or more rounds up
- Large numbers: fill with zeros (38 600 to 1 s.f. = 40 000)
- Truncate: cut off the digits, never round up
What are significant figures?
Significant figures measure accuracy from the first non-zero digit. In 5832 the first significant figure is 5; in 0.00408 it is 4, because the leading zeros are only placeholders. Zeros between non-zero digits do count, so 0.00408 has three significant figures: 4, 0 and 8.
Rounding to significant figures
Count the required number of significant figures from the first non-zero digit, then look at the next digit to decide whether to round up. 5832 to 2 significant figures keeps 5 and 8, the next digit is 3, so it rounds down to 5800.
Keeping the size of the number
For large numbers, fill the remaining places with zeros so the number keeps its value: 38 600 to 1 significant figure is 40 000, not 4. For small numbers, keep the leading zeros: 0.008396 to 2 significant figures is 0.0084. Rounding up can carry into the next column, so 0.0996 to 2 significant figures is 0.10.
Truncation
Truncating cuts off digits after a certain point, without rounding. 3.78 truncated to 1 decimal place is 3.7, while rounding would give 3.8. Some displays and meters work this way, and so does stating a person's age in whole years.
Giving calculator answers
When a question says “give your answer to 3 significant figures”, write down a few more digits from the calculator first, then round. Writing the unrounded value shows the examiner your working and protects the method mark.
Worked examples
Example 1. Round 5832 to 2 significant figures.
- The first two significant figures are 5 and 8; the next digit is 3.
- 3 rounds down, and zeros keep the place value.
Answer: 5800.
Example 2. Round 0.008396 to 2 significant figures.
- The first significant figure is 8, the second is 3; the next digit is 9.
- 9 rounds the 3 up to 4.
Answer: 0.0084.
Example 3. Round 38 600 to 1 significant figure.
- The first significant figure is 3; the next digit is 8.
- Round up to 4 and fill with zeros.
Answer: 40 000.
Example 4. Truncate 3.78 to 1 decimal place, and compare with rounding.
- Truncating cuts off the 8 without changing the 7.
- Rounding would look at the 8 and round up.
Answer: Truncated: 3.7. Rounded: 3.8.
Example 5. Work out √41.7, giving your answer to 3 significant figures.
- The calculator gives 6.45755…
- The fourth significant figure is 7, so round up.
Answer: 6.46.
Common mistakes
- Counting leading zeros. In 0.0084 the first significant figure is 8.
- Dropping the zeros in large numbers. 38 600 to 1 s.f. is 40 000, not 4.
- Rounding when asked to truncate. Truncation never rounds up: 3.78 becomes 3.7.
- Rounding in two stages. Round the original value once.
- Not showing the unrounded value. Write down the full calculator answer before rounding.
How significant figures are examined
Rounding to significant figures is a Foundation skill in Edexcel GCSE (1MA1) and the 4MA1 International GCSE, and accurate rounding is expected in final answers on every calculator paper. Questions ask you to:
- round a large or small number to a given number of significant figures
- truncate a value and compare it with rounding
- give a calculator answer to 3 significant figures
- use 1 significant figure rounding to estimate
Practise with the rounding and estimation worksheet, which includes answers, and the GCSE number revision engine.
Significant figures are used in estimating calculations, and truncation leads to error intervals.
Frequently asked questions
What is the first significant figure?
The first non-zero digit, reading from the left.
Do zeros count as significant figures?
Zeros at the start of a decimal do not. Zeros between other digits do. Trailing zeros in a whole number usually just hold the place.
What is the difference between rounding and truncating?
Rounding can go up or down depending on the next digit; truncating always cuts the digits off.