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

1 Answer
Sep 3, 2016

Answer:

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.