# 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

a. 0.005032 x 4.0009

b. 0.0080750 / 10.037

##### 1 Answer

Sep 3, 2016

Here are the five rules you need.

#### Explanation:

- All
#color (red)("non-zero digits")# **are significant**. #color(red)("Leading zeroes")# are**not significant**.#color(red)("Zeroes between significant digits")# **are significant**.#color(red)("Trailing zeroes in the decimal portion")# of a number**are significant**.- 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.