Ever wondered why reporters say "about 46,000 fans"?

The gate count at a match in Kano was 45,678. A reporter rounds it to 46,000 — keeping just the 2 most important digits. Those important digits are called significant figures.

📒 Significant Figures: lesson notes

Learn which digits count as significant and round big and small numbers to 1, 2 or 3 significant figures.

The gate count at a match in Kano was 45,678. A reporter rounds it to 46,000 — keeping just the 2 most important digits. Those important digits are called significant figures.

Which digits are significant?

Significant figures (s.f.) are the digits that carry the meaning of a number. Start counting at the first non-zero digit.

Zeros at the start of a decimal only show place value, so they do not count: 0.0047 has 2 significant figures (4 and 7).

Zeros between non-zero digits do count: 3.05 has 3 s.f. A zero at the end of a decimal also counts: 2.50 has 3 s.f., because it shows the number is accurate to hundredths.

🔑 Key idea: Start counting at the first non-zero digit.

Rounding to significant figures

Count the significant figures you need, then look at the next digit: 5 or more → round up; 4 or less → round down.

45,678 to 2 s.f.: keep 4 and 5; the next digit is 6, so round up to 46. Then fill the other places with zeros: 46,000.

The zeros matter! 46 is not the same as 46,000 — the rounded number must stay about the same size.

🔑 Key idea: Round, then fill the whole-number places with zeros.

Small numbers

For 0.004736 to 2 s.f., skip the leading zeros. The first two significant figures are 4 and 7, and the next digit is 3, so round down: 0.0047.

Do not add zeros at the end of a small decimal after rounding — 0.0047 is already the right size.

Compare with decimal places: 0.004736 to 2 decimal places is 0.00. Significant figures are much more useful for tiny numbers.

🔑 Key idea: Leading zeros are never significant.

Worked example

Write 0.8861 correct to 1 significant figure.

Step 1: Find the first significant figure
The first non-zero digit is 8.
Step 2: Keep 1 significant figure
The first 1 significant figure is 8.
The next digit is 8: 5 or more, so round UP.
Step 3: Answer
0.8861 ≈ 0.9 (1 s.f.)

Answer: 0.9

Summary

Start counting significant figures at the first non-zero digit.
Leading zeros never count; zeros between digits always count; a final zero in a decimal counts.
Round using the next digit: 5 or more rounds up.
Fill whole-number places with zeros so the size stays the same: 45,678 ≈ 46,000 (2 s.f.).

Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.