Find the first significant digit first
In 0.00473, the first significant digit is 4 because the zeros only hold place value.
Leading zeros are not significant because they only position the decimal.
Year 8
Rounding to significant figures
Round numbers to significant figures accurately, identify the first significant digit, and use approximation to check whether answers are sensible.
Lesson overview
Number - place value, approximation and accuracy
Significant figures begin with the first non-zero digit. To round to a chosen number of significant figures, keep the required digits, look at the next digit, then round up or stay the same. This matters in science, finance and estimation because it controls the level of accuracy being communicated.
The next digit decides the rounding
To round 5831 to 2 significant figures, keep 58 and check the next digit, which is 3.
If the next digit is 5 or more, round up. If it is 4 or less, keep the kept digit unchanged.
Approximation checks whether an answer is sensible
If 198 x 31 is estimated as 200 x 30, the answer should be close to 6000.
| Exact calculation | Rounded estimate | Approximate answer |
|---|---|---|
| 198 x 31 | 200 x 30 | 6000 |
A quick estimate helps you spot answers that are far too large or far too small.
Worked example
Round 0.07846 to 2 significant figures.
| Digits | First 2 significant figures | Next digit | Rounded result |
|---|---|---|---|
| 0 0 7 8 4 6 | 7 and 8 | 4 | 0.078 |
- Ignore the leading zeros and start counting significant figures from 7.
- Keep the first two significant figures, which are 7 and 8.
- Look at the next digit, which is 4, so do not round up.
- Write the rounded answer as 0.078.
Try it
Identify the first significant digit before you decide where the rounding point sits.
Question 1
Round 4729 to 2 significant figures.
Question 2
Round 0.00651 to 2 significant figures.
Question 3
Round 5831 to 1 significant figure.
Question 4
Which estimate is sensible for 201 x 49?
| Rounded numbers | Estimate |
|---|---|
| 200 x 50 | 10000 |
Question 5
Which statement is correct?
Common mistakes
Watch for these when working through the lesson.
- Starting to count significant figures from a leading zero.
- Rounding from the wrong digit.
- Changing the size of the number too much when writing the rounded answer.
Related topics
These ideas fit closely with this lesson.
- Percentages of amounts without a calculator.
- Ratio scaling, simplifying and sharing in a ratio.
- Plot and interpret linear graphs from y = mx + c.