# How can I perform the following operation 100-23, taking into account the number of significant figures?

Oct 6, 2016

The answer is either 77 or 100, depending on whether the numbers were obtained by counting or by measurement.

#### Explanation:

If obtained by counting

All digits obtained by counting are significant.

$\text{100 apples - 23 apples = 77 apples}$.

Thus, $\text{100 - 23 = 77}$, and the answer has two significant figures.

If obtained by measurement

Trailing zeroes are not significant in numbers without decimal points.

Thus, a measurement of $\text{100 g}$ means 1 × 10^2color(white)(l) "g" (1 significant figure).

A measurement of $\text{23 g}$ means 0.27 × 10^2color(white)(l) "g" (2 significant figures).

$\text{100 g - 23 g" = 1 × 10^2 color(white)(l)"g" - 0.23 × 10^2color(white)(l) "g" = "(1 - 0.23)" × 10^2 color(white)(l)"g" = 0.77 × 10^2 color(white)(l)"g}$

The rules for adding and subtracting are that you must round off so the answer has no more digits after the decimal place than the number with the fewest digits after the decimal place.

Thus, $\text{1 - 0.23} = 0.77$ must be rounded so there are no digits after the decimal place:

To the closest unit, $\text{1 - 0.23} = 1$.

$\text{100 g - 23 g = 100 g}$ (1 significant figure) and

$\text{100 - 23} = 100$