What are significant figures ?

Significant figures, also called significant digits, are digits that represent an actual measurement. Nonzero digits such as 1, 2, 3, 4, 5, 6, 7, 8, and 9 are always significant figures.

Example #1

The weight of a penny is 2.5 grams.

2 and 5 are significant digits since they represent digits of the actual measurement. When we put the coin on the balance scale, the display will show 2.5 grams. In kilograms, the weight is 0.0025 kg. The three zeros on the left of 2 and 5 are not significant digits because they were not there in the actual measurement. The significant digits are still 2 and 5.

Example #2

If you go on a balance scale to measure your weight and the display shows 150 pounds, 1,5, and 0 are all significant digits. If we remove the 0, then this is not the actual measurement of your weight.

Example #3

Suppose you measure the weight of a book and you find out that it is 2 kg. In grams, the weight is now 2000 grams. Unlike example #2,  the three zeros next to the 2 are not significant figures because in the actual measurement, they did not exit. Therefore, 2 kg has 1 significant digit and 2000 grams still have 1 significant digit. The significant digit or figure is 2.

Rules for significant figures

The following table will help you find significant figures and see whether or not a zero is a significant digit.

Type of number Significant figures Example
positive integers Zeros between nonzero digits are significant. Zeros to the right of all nonzero digits are not significant (Unless specifically known to be such as example # 2 above). 306000 : 3 significant digits.
Decimal numbers between 0 and 1 Zeros to the left of all the nonzero digits are not significant. All other zeros are significant. 0.000408010 : 6 significant digits
noninteger decimal numbers greater than 1 All zeros are significant 460.040710 : 9 significant digits

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