Question

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

Answer 1

Here are the five rules you need.

Explanation:

1. All `color (red)("non-zero digits")` are significant.
2. `color(red)("Leading zeroes")` are not significant.
3. `color(red)("Zeroes between significant digits")` are significant.
4. `color(red)("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"` `color(red)("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.