# Without calculating the result, how do you find the number of significant figures in the following products and quotients?

## a. 0.005032 x 4.0009 b. 0.0080750 / 10.037

Sep 3, 2016

#### Answer:

Here are the five rules you need.

#### Explanation:

1. All $\textcolor{red}{\text{non-zero digits}}$ are significant.
2. $\textcolor{red}{\text{Leading zeroes}}$ are not significant.
3. $\textcolor{red}{\text{Zeroes between significant digits}}$ are significant.
4. $\textcolor{red}{\text{Trailing zeroes in the decimal portion}}$ of a number are significant.
5. In multiplication and division, color(red)("you round the answer to have the same number of significant digits as the number" $\textcolor{red}{\text{with the fewest significant figures}}$.

a. 0.005032 × 4.0009

In 0.005032, there are three leading zeroes (not significant) and one zero between significant digits, for a total of four significant digits.

In 4.0009, there are three zeroes between significant digits, for a total of five significant digits.

b. 0.0080750/10.037

In 0.0080750, there are three leading zeroes (not significant) and one zero between significant digits, and one trailing zero in the decimal (significant), for a total of five significant digits.

In 10.037, there are two zeroes between significant digits, for a total of five significant digits.