significant figures addition subtraction multiplication and division

Significant Figures

1. Zeros at the end or right of a number are significant provided they are on the right side of the decimal point. Otherwise, the zeros are not significant.
For example, 0.200 g has three significant figures.But100 has only one significant figure.

2. Zeros preceding to first non-zero digit are not significant. Such zero indicates the position of decimal point.
Example:
0.03 has one significant figure
0.0052 has two significant figures.

3. When numbers are written in scientific notation, the number of digits between 1 and 10 gives the number of significant figures
Examples:
4.01×10² has three significant figures,
8.256 × 10^–3 has four significant figures.

4. Zeros between two non-zero digits are significant. Thus, 2.005 has four significant figures.

Addition and Subtraction of Significant Figures

The result cannot have more digits to the right of the decimal point than either of the original numbers.
Here, 18.0 has only one digit after the decimal point and the result should be reported only up to one digit after the decimal point which is 31.1.

Addition and Subtraction of Significant Figures

Multiplication and Division of Significant Figures

In these operations, the result must be reported with no more significant figures as are there in the measurement with the few significant figures.
2.5×1.25 = 3.125
Since 2.5 has two significant figures, the result should not have more than two significant figures, thus, it is 3.1