Significant figures are the important digits in a number, starting from the first digit that is not zero.
The easiest rule to remember is:
Start counting from the first non-zero digit.
For example:
4 7 2 8
Every digit is significant.
So:
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.
The zeros at the beginning are only showing us where the decimal point is. They are not significant figures.
There isn’t really a formula for significant figures. Instead, use this simple method:
Find → Count → Check → Round
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
✏️ Example Math 1 — Easy
Round 4728 to 2 significant figures.
Step 1: Find the first non-zero digit.
The first digit is 4.
Step 2: Count 2 significant figures.
4 7 | 2 8
We want to keep 47.
Step 3: Look at the next digit.
The next digit is 2.
Because:
2 < 5
we do not round 7 up.
Therefore:
4728 ≈ 4700
Answer:
4700 (2 SF)
✏️ Example Math 2 — Rounding Up
Round 7863 to 2 significant figures.
Count from the first non-zero digit:
7 8 | 6 3
We want to keep 78.
Now look at the next digit.
It is 6.
Since:
6 ≥ 5
we round the 8 up to 9.
So:
7863 ≈ 7900
Answer:
7900 (2 SF)
✏️ Example Math 3 — Decimal Number
Round 6.4837 to 3 significant figures.
Start with the first non-zero digit:
6 . 4 8 | 3 7
The first 3 significant figures are:
6, 4, 8
The next digit is 3.
Since:
3 < 5
the 8 stays the same.
Answer:
6.48 (3 SF)
✏️ Example Math 4 — Small Decimal
Round 0.007856 to 2 significant figures.
Don’t start counting from the zeros.
Find the first non-zero digit:
0.00 7 8 | 5 6
- 7 = 1st SF
- 8 = 2nd SF
- next digit = 5
Since the next digit is 5, round the 8 up.
So:
0.007856 ≈ 0.0079
Answer:
0.0079 (2 SF)
Notice something important:
The zeros before the 7 do not count as significant figures.
✏️ Example Math 5 — A Zero Can Be Significant
Round 5.0678 to 3 significant figures.
Start counting from 5:
5 . 0 6 | 7 8
Now count:
- 5 = 1st SF
- 0 = 2nd SF
- 6 = 3rd SF
The zero does count here because it is between significant digits.
The next digit is 7.
Since:
7 ≥ 5
round 6 up to 7.
Answer:
5.07 (3 SF)
🔍 Significant Figures vs Decimal Places
Do not confuse significant figures (SF) with decimal places (DP).
Consider:
0.004726
To 2 significant figures:
Start counting from the first non-zero digit:
0.00 4 7 | 2 6
Answer:
0.0047
To 2 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
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 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
Tip 2 — Never count leading zeros
For:
0.000529
your counting starts at 5, not at the first zero.
0.000 5 2 9
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.
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.
⚠️ Common Mistakes
Mistake 1 — Counting zeros before the first non-zero digit
❌ 0.00346
Thinking:
0 = 1st SF
This is wrong.
Start at 3:
0.00 3 4 6
So the number has 3 significant figures.
Mistake 2 — 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 3 — 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 4 — 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 and Answer
Try these yourself before looking at the answers.
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
🎯 Quick Revision Box
Remember these four steps:
1. FIND the first non-zero digit.
2. COUNT the required significant figures.
3. CHECK the next digit.
4. ROUND: 0–4 stay, 5–9 round up.
And remember the most important difference:
Significant Figures → start at the first non-zero digit.
Decimal Places → start immediately after the decimal point.
Once you can quickly find that first non-zero digit, significant-figure questions become much easier. 📘✨
Want to Explore This Topic Further?
Select a topic below to continue learning.
