What are Significant Figures?

Significant figures are the numbers in a value that tell us how exact or accurate the number is. They help us know which digits are important when measuring or calculating.

• To show how precise a number is.


• To make calculations easier.


• To avoid writing unnecessary digits.


• To check if an answer is reasonable.

• All non-zero digits are significant.


• Example: 123 → 3 significant figures


• Example: 7.56 → 3 significant figures


• Zeros between non-zero digits are significant.


• Example: 102 → 3 significant figures


• Example: 5006 → 4 significant figures


• Leading zeros are NOT significant.


• Example: 0.00456 → 3 significant figures


• Example: 0.00072 → 2 significant figures


• Trailing zeros in a decimal number are significant.


• Example: 3.400 → 4 significant figures


• Example: 0.0500 → 3 significant figures


• Trailing zeros in a whole number without a decimal point are unclear.


• Example: 500 → 1, 2, or 3 significant figures (depends on context)

Step-by-Step Guide:

1. Decide how many significant figures you want.


2. Count from the first non-zero digit.


3. Look at the next digit (the rounding digit).


4. If it is 5 or more, increase the last significant digit by 1.


5. If it is less than 5, leave the last significant digit as it is.


6. Remove or change all digits after the last significant figure.

Examples:

• 3467 to 2 s.f. → 3500


• 0.004563 to 2 s.f. → 0.0046


• 12.345 to 3 s.f. → 12.3


• 0.05678 to 3 s.f. → 0.0568


• 98765 to 4 s.f. → 98770

Using Significant Figures in Calculations

• Multiplication & Division: The answer should have the same number of significant figures as the number with the fewest significant figures.


• Example: 3.24 × 2.1 → 6.8 (2 s.f.)


• Addition & Subtraction: The answer should have the same number of decimal places as the number with the fewest decimal places.


• Example: 12.11 + 0.3 → 12.4 (1 decimal place)

Common Mistakes

• Counting leading zeros as significant.


• Forgetting that zeros at the end of a decimal number are significant.


• Mixing up significant figures with decimal places.


• Not rounding correctly after calculations.


• Using too many or too few significant figures in answers.

1. Example 1: Count the significant figures in 0.00709.
   
   Step 1: Ignore all leading zeros (0.00).
   
   Step 2: The remaining digits are 7, 0, 9.
   
   Answer: 3 significant figures.
   
   


2. Example 2: Round 0.004678 to 2 significant figures.
   
   Step 1: Identify the first 2 significant digits → 4 and 6.
   
   Step 2: Look at the next digit (7) to round → 6 rounds up to 7.
   
   Answer: 0.0047
   
   


3. Example 3: Round 12,845 to 3 significant figures.
   
   Step 1: First 3 significant digits → 1, 2, 8.
   
   Step 2: Next digit is 4 → less than 5, do not round up.
   
   Step 3: Replace remaining digits with zeros.
   
   Answer: 12,800
   
   


4. Example 4: Count the significant figures in 5006.
   
   Step 1: All non-zero digits are significant (5 and 6).
   
   Step 2: Zeros between non-zero digits are also significant.
   
   Answer: 4 significant figures
   
   


5. Example 5: Round 0.05078 to 3 significant figures.
   
   Step 1: First 3 significant digits → 5, 0, 7.
   
   Step 2: Next digit is 8 → round up the last significant digit 7 → 8.
   
   Answer: 0.0508
   
   


6. Example 6: Multiply 4.32 × 1.6 using significant figures.
   
   Step 1: 4.32 has 3 s.f., 1.6 has 2 s.f.
   
   Step 2: Perform the multiplication: 4.32 × 1.6 = 6.912
   
   Step 3: Round the answer to 2 s.f. (fewest significant figures) → 6.9
   
   Answer: 6.9
   
   


7. Example 7: Add 12.145 + 0.3 using decimal places.
   
   Step 1: 12.145 has 3 decimal places, 0.3 has 1 decimal place.
   
   Step 2: Addition: 12.145 + 0.3 = 12.445
   
   Step 3: Round to 1 decimal place (fewest decimal places) → 12.4
   
   Answer: 12.4
   
   


8. Example 8: Round 0.009876 to 2 significant figures.
   
   Step 1: First 2 significant digits → 9 and 8.
   
   Step 2: Next digit is 7 → round up 8 → 9.
   
   Answer: 0.0099
   
   


9. Example 9: Round 987,654 to 4 significant figures.
   
   Step 1: First 4 significant digits → 9, 8, 7, 6.
   
   Step 2: Next digit is 5 → round up 6 → 7.
   
   Step 3: Replace remaining digits with zeros.
   
   Answer: 987,700
   
   


10. Example 10: Count the significant figures in 0.0045000.
    
    Step 1: Ignore leading zeros → 4, 5, 0, 0, 0 remain.
    
    Step 2: All trailing zeros in a decimal number are significant.
    
    Answer: 5 significant figures
    
    

Conclusion

Significant figures help us show how exact a number is. They are very important in measurement, calculation, and daily life. Using significant figures correctly avoids mistakes and makes answers easy to understand.