Approximations

Significant Figures: The number of digits in a measurement about which we are certain plus one additional digit which is uncertain are known as significant figures.

Thus, in cm, there are four significant figures. Similarly, have significant digits.

Rules for Finding the Number of Significant Figures

Rule 1: All non-zero digits in a measurement are significant.

*Example: ** *g has five significant figures. m has three significant figures.

Rule 2: In a decimal number which is greater than , all digits (including zeros) are significant.

*Example:*

- kg has six significant figures.
- has four significant figures.
- has three significant figures
- km has six significant figures

Rule 3: In a decimal number which lies between 0 and 1, all zeros to the right of the decimal point but to the left of the· first non-zero digit are not significant

*Example: ** km has only significant figures while kg has significant figures*.

Rule 4: If the measurement is a whole number, then the case becomes ambiguous if there are zeros to the left of an understood decimal point but to right of a non-zero digit.

Rule 5: All the final zeros in a decimal number obtained by rounding off a decimal to a given number of decimal places are significant.

*Example: when is rounded off to two decimal places, we get , which has three significant figures*

Rounding off a Decimal to the Required Number of Significant Figures

Sometimes during measurements it is required to obtain the value of a decimal number correct to the required number of significant figures.

*Example: Round kg to three significant figures:*

*Solution: The measurement kg has significant figures. To round it off to significant figures, we are required to round it off to place after the decimal. Therefore kg = kg rounded off to significant figures.*

Rounding off to a Specified Unit

*Example: **Round off: Rs. to the nearest rupees. **Rs. Rs. rounded to the nearest rupees.*