Significant Figures (SF)
Significant figures, often written as SF or s.f., are the digits in a number that tell us how accurate or precise that number is.
Significant figures are the important digits in a number, starting from the first digit that is not zero.
The easiest rule to remember is:
For example: 4 7 2 8
So:
- 4 is the 1st SF
- 7 is the 2nd SF
- 2 is the 3rd SF
- 8 is the 4th SF
Therefore: 4728 has 4 significant figures.
What about zeros?
This is where students often get confused.
Look at: 0.00472
Do not start counting from the zeros.
Find the first non-zero digit, which is 4.
So: 0.00 4 7 2
- 4 = 1st SF
- 7 = 2nd SF
- 2 = 3rd SF
Therefore: 0.00472 has 3 significant figures.
There isn’t really a formula for significant figures. Instead, use this simple method:
Step 1 — FIND
Find the first non-zero digit.
Step 2 — COUNT
Starting from that digit, count the number of significant figures required.
Step 3 — CHECK
Look at the next digit.
Step 4 — ROUND
Use the normal rounding rule:
0, 1, 2, 3, 4 → keep the previous digit the same
5, 6, 7, 8, 9 → increase the previous digit by 1
A useful memory trick is:
0–4 → stay
5–9 → round up
Do not confuse significant figures (SF) with decimal places (DP).
Consider:
0.004726 – Let’s find out SF and DP of the same number!
Let’s find out two significant figure:
Start counting from the first non-zero digit:
0.00 4 7 | 2 6
Answer:
0.0047
Let’s find out two decimal places:
Start counting after the decimal point:
0 . 0 0 | 4 7 2 6
The third decimal digit is 4, so:
0.00
These give completely different answers.
SF → start from the first non-zero digit.
DP → start immediately after the decimal point.
Exam Tip 1 — Circle the required digit
If the question says:
Round 38.647 to 3 significant figures.
Count:
3 8 6 | 4 7
The third significant figure is 6.
Circle or underline or color that digit:
38.647
Then look one digit to the right.
That digit tells you whether to round up.
Because it is 4, the answer is:
38.6
Exam Tip 2 — Never count leading zeros
For:
0.000529
your counting starts at 5, not at the first zero.
0.000 5 2 9
Exam Tip 3 — Keep the correct place value
Suppose:
Round 63 728 to 2 SF.
You cannot write:
64
The original number is about sixty-four thousand, not sixty-four.
Correct:
63 728 ≈ 64 000
The zeros are needed to keep the number at the correct size.
Exam Tip 4 — Don’t round too early in calculations
If a question contains several calculations, keep the full calculator value during your working.
Round only the final answer, unless the question specifically tells you otherwise.
Early rounding can change your final answer.
Mistake 1 — Confusing SF with DP
Round 0.05678 to 2 SF.
❌ Wrong idea: count two places after the decimal point.
Instead:
0.0 5 6 | 7 8
5 = 1st SF
6 = 2nd SF
7 tells us to round up.
✅ Answer:
0.057
Mistake 2 — Looking at the wrong digit
Round 4.376 to 2 SF.
Keep:
4.3
But you must look at the next digit, which is 7.
Since 7 ≥ 5:
4.3 → 4.4
✅ Answer: 4.4
Mistake 3 — Removing necessary zeros
Round 5827 to 2 SF.
The first two significant figures are 5 and 8.
The next digit is 2, so 58 stays.
But:
❌ 58
is wrong.
You need the zeros to preserve the place value:
✅ 5800
Question 1
Round 3847 to 2 significant figures.
Answer: 3800
Why?
3 8 | 4 7
The next digit is 4.
4 < 5, so 8 stays the same.
3847 ≈ 3800
Question 2
Round 7586 to 3 significant figures.
Answer: 7590
Why?
7 5 8 | 6
The next digit is 6.
6 ≥ 5, so the 8 rounds up to 9.
7586 ≈ 7590
Question 3
Round 4.7638 to 3 significant figures.
Answer: 4.76
Why?
4 . 7 6 | 3 8
The next digit is 3.
3 < 5.
Therefore:
4.7638 ≈ 4.76
Question 4
Round 0.008476 to 2 significant figures.
Answer: 0.0085
Why?
Ignore the leading zeros:
0.00 8 4 | 7 6
8 = 1st SF
4 = 2nd SF
The next digit is 7, so 4 rounds up to 5.
0.008476 ≈ 0.0085
Question 5
Round 92 649 to 3 significant figures.
Answer: 92 600
Why?
9 2 6 | 4 9
The next digit is 4.
4 < 5, so 6 stays the same.
92 649 ≈ 92 600
Question 6 — Challenge 🔥
A calculator gives:
0.00398726
Write the answer correct to 3 significant figures.
Start counting at the first non-zero digit:
0.00 3 9 8 | 7 2 6
The first three significant figures are 3, 9, 8.
The next digit is 7, so the 8 rounds up to 9.
Answer:
0.00399