Explain all the rules for significant figures with suitable examples.

📘 Significant Figures

Significant figures are the digits in a measured quantity that carry meaningful information about its precision.

They include all the certain digits plus the first uncertain digit of a measurement.

🎬 Significant Digits Visualization

2 . 3 4 5

The highlighted digit represents the last significant measured digit.

1️⃣ All Non-Zero Digits Are Significant

All digits from 1 to 9 are always significant.

Example: 347 → 3 significant figures

Example: 58.29 → 4 significant figures

2️⃣ Zeros Between Non-Zero Digits Are Significant

A zero placed between two non-zero digits is always significant.

105 → 3 significant figures

2.05 → 3 significant figures

1002 → 4 significant figures

3️⃣ Leading Zeros Are NOT Significant

Zeros before the first non-zero digit are called leading zeros. They are not significant.

0.0045 → 2 significant figures

0.00072 → 2 significant figures

They only indicate the position of the decimal point.

4️⃣ Zeros Between Digits Are Significant

Zeros occurring between non-zero digits are counted.

3.007 → 4 significant figures

40.05 → 4 significant figures

5️⃣ Trailing Zeros After a Decimal Are Significant

Zeros at the end of a number are significant when a decimal point is present.

2.50 → 3 significant figures

4.700 → 4 significant figures

0.0600 → 3 significant figures

6️⃣ Trailing Zeros in a Whole Number Without Decimal

Trailing zeros in a whole number without a decimal point can be ambiguous.

1500 → significance is ambiguous

Use scientific notation to clearly show the number of significant figures.

1.5 × 10³ → 2 significant figures

1.50 × 10³ → 3 significant figures

1.500 × 10³ → 4 significant figures

7️⃣ Exact Numbers Have Unlimited Significant Figures

Numbers obtained by counting or exact definitions are considered exact and do not limit significant figures.

12 students → exact number

1 dozen = 12 → exact definition

8️⃣ Scientific Notation

In scientific notation, all digits in the coefficient are significant.

3.45 × 10⁵ → 3 significant figures

6.020 × 10²³ → 4 significant figures

9.00 × 10⁻³ → 3 significant figures

🔄 Rule 9: Rounding Off

When reducing the number of significant figures:

• If the next digit is 5 or greater, increase the retained digit by 1.
• If the next digit is less than 5, leave the retained digit unchanged.

4.376 → 3 significant figures
= 4.38

4.372 → 3 significant figures
= 4.37

➕ Rule 10: Addition & Subtraction

For addition and subtraction, the answer should have the same number of decimal places as the number with the fewest decimal places.

12.11 + 18.2 + 3.456

18.2 has only 1 decimal place.

= 33.766
≈ 33.8

✖️ Rule 11: Multiplication & Division

For multiplication and division, the final answer should have the same number of significant figures as the quantity having the fewest significant figures.

2.5 × 3.42 = 8.55

2.5 has 2 significant figures.

Answer = 8.6

🧮 Complete Example

How many significant figures are present in:

0.0040500

Ignore the leading zeros. The significant digits are:

4 0 5 0 0

✅ 0.0040500 has 5 significant figures.

🎯 Quick Revision

Number	Significant Figures
347	3
105	3
0.0045	2
2.50	3
6.020 × 10²³	4

💡 Remember

Non-zero digits → Always significant
Zeros between non-zero digits → Significant
Leading zeros → Not significant
Trailing decimal zeros → Significant