Significant figures tell us how precise a measurement is. In science and physics, you don’t just write numbers — you show how accurate those numbers are. That’s where significant figures come in.
Many students lose marks not because they don’t know the rules, but because they miscount significant figures in measurements. Let’s fix that properly.
What Are Significant Figures in Measurements?
Significant figures (sig figs) are the digits in a measurement that include:
- All certain digits
- Plus one uncertain (estimated) digit
They show the precision of the measuring instrument.
Example:
If a ruler measures up to the nearest millimeter, your measurement is only reliable to that level — not beyond.
Step 1: Start Counting from the First Non-Zero Digit
This is the golden rule.
Example:
- 0.00456 → 3 significant figures
- Start counting from 4, not from zeros.
❌ Leading zeros are never significant
✅ They only help place the decimal
Step 2: All Non-Zero Digits Are Always Significant
Any number from 1 to 9 is significant.
Examples:
- 27 → 2 significant figures
- 4.892 → 4 significant figures
- 98.01 → 4 significant figures
This rule never changes.
Step 3: Zeros Between Non-Zero Digits Are Significant
These are called captive zeros.
Examples:
- 1002 → 4 significant figures
- 3.05 → 3 significant figures
- 7.001 → 4 significant figures
Zeros trapped between real numbers always count.
Step 4: Trailing Zeros Depend on the Decimal Point
This is where most mistakes happen.
Without a decimal point:
- 1500 → 2 significant figures
(zeros are NOT significant)
With a decimal point:
-
- → 4 significant figures
- 15.00 → 4 significant figures
👉 Decimal point makes zeros meaningful
Step 5: Zeros After the Decimal Are Significant (If They Follow a Number)
Examples:
- 2.40 → 3 significant figures
- 0.560 → 3 significant figures
- 6.00 → 3 significant figures
These zeros show measurement precision, so they count.
Step 6: Exact Numbers Have Infinite Significant Figures
Some numbers are defined, not measured.
Examples:
- 1 dozen = 12
- 1 m = 100 cm
- Number of students in a class
These have unlimited significant figures and don’t limit calculations.
Common Measurement Examples (Quick Practice)
| Measurement | Significant Figures |
|---|---|
| 0.030 | 2 |
| 4.070 | 4 |
| 250 | 2 |
| 250.0 | 4 |
| 9.8 | 2 |
Quick Trick to Check Yourself
Ask this question:
Did the measuring tool allow me to know this digit for sure?
If yes → count it
If no → don’t
Final Tip for Exams
- Always count sig figs before calculations
- Round only at the final answer
- Never guess extra precision
Mastering significant figures is not about memorizing rules — it’s about understanding measurement accuracy.
FAQs
How to Properly Use Significant Figures?
Answer:
To properly use significant figures, first count the number of significant figures in each given value. During calculations, keep extra digits, but round the final answer only to the required number of significant figures.
For multiplication and division, the result should have the same number of significant figures as the value with the fewest significant figures.
For addition and subtraction, the result should have the same number of decimal places as the value with the fewest decimal places.
How Do You Write 0.416 666 667 Correctly to 3 Significant Figures?
Answer:
Given number: 0.416 666 667
- The first three significant digits are 4, 1, and 6
- The next digit is 6, which is greater than 5, so rounding is required
Correct answer:
0.417
What Is 432.75 Rounded to 2 Significant Figures?
Answer:
Given number: 432.75
- The first two significant digits are 4 and 3
- The next digit is 2, which is less than 5, so no rounding up is needed
Correct answer:
430
(The zero is not significant; it only shows the size of the number.)
What Is 0.9999 Rounded to 3 Significant Figures?
Answer:
Given number: 0.9999
- The first three significant digits are 9, 9, and 9
- The next digit is 9, which causes rounding up
Correct answer:
1.00
(The two zeros after the decimal indicate that the value has three significant figures.)