Significant Figures – Units and Measurement

Significant Figures: In the measured value of a physical quantity, the number of digits about the correctness of which we are sure plus the next doubtful digit, are called the significant figures.

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Significant Figures – Units and Measurement

Rules for Finding Significant Figures

1. All non-zeros digits are significant figures, e.g. 4362 m has 4 significant figures.
2. All zeros occuring between non-zero digits are significant figures, e.g. 1005 has 4 significant figures.
3. All zeros to the right of the last non-zero digit are not significant, e.g. 6250 has only 3 significant figures.
4. In a digit less than one, all zeros to the right of the decimal point and to the left of a non-zero digit are not significant, e.g. 0.00325 has only 3 significant figures.
5. All zeros to the right of a non-zero digit in the decimal part are significant, e.g. 1.4750 has 5 significant figures.

Significant Figures in Algebraic Operations
(i) In Addition or Subtraction:
In addition or subtraction of the numerical values, the final result should retain as many decimal places as there are in the number with the least places. e.g.
If l₁ = 4.326 m and l₂ = 1.50 m
Then, l₁ + l₂ =(4.326 + 1.50) m = 5.826 m
As l₂ has measured upto two decimal places, therefore
l₁ + l₂ = 5.83 m

(ii) In Multiplication or Division:
In multiplication or division of the numerical values, the final result should retain as many significant figures as there are in the original number with the least significant figures, e.g. If length l = 12.5 m and breadth b = 4.125 m.
Then, area A = l x b = 12.5 x 4.125 = 51.5625 m²
As l has only 3 significant figures, therefore
A = 51.6 m²

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.