Core Concept

Significant figures, also known as significant digits or sig figs, provide a way to convey the reliability and limitations of measurements and calculations. They indicate the precision of a measurement and convey the level of certainty or uncertainty associated with it. 

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• Counting Significant Figures

  1. Using Significant Figures in Addition and Subtraction

  2. Using Significant Figures in Multiplication and Division

In general, the following guidelines are followed when determining significant figures:

3 Rules when counting significant figures:

1. If there is a decimal point present -- start at the LEFT and count, beginning with the first non-zero digits. 

Examples: 340. 3 significant figures

30400. 5 significant figures

0.34955 5 significant figures

0.00500 3 significant figures

1. If there is NOT a decimal point present -- start at the RIGHT and count, beginning with the first non-zero digit. 

Examples: 340 2 significant figures 

30400 3 significant figures

34955 5 significant figures

2. Counting numbers, conversions and accepted values have unlimited (infinite) significant figures).

• Non-zero digits are always significant. For example, the number 23.45 has four significant figures.

  1. Leading zeros (zeros to the left of the first non-zero digit) are not significant. For example, in the number 0.0052, only the digits 5 and 2 are significant, so it has two significant figures.

  2. Trailing zeros (zeros to the right of the last non-zero digit) can be significant or insignificant, depending on whether they are measured or merely placeholders. For example, in the number 120.0, the zero after the decimal point indicates that the measurement is precise to the tenths place, so it has four significant figures. In contrast, the number 120 has only two significant figures because the zero is not measured but acts as a placeholder.

  3. Zeros between non-zero digits are always significant. For example, the number 502 has three significant figures.