1 Skills, Methods, and the Nature of Physics - BC Science Physics 11

Multiplying or Dividing Measurements
You measure the dimensions of a wall to be 8.53 m × 2.74 m. What is the area of the wall?
Imagine your calculator battery is dead, and you have to multiply the old-fashioned way.
In the two measurements, the last digit is uncertain, so any product involving either of
these two digits will also be uncertain.
8.53 m
× 2.74 m
3412
5971
1706
23.3722 m 2 ≅ 23.4 m 2
Since the 3 following the decimal is an uncertain digit, all digits following it are
meaningless. Round off the .3722 to .4, and write 23.4 m 2 for the area of the wall.
Use the following common sense rule when multiplying or dividing measurements:
When multiplying or dividing measurements, the product or quotient must have
no more significant digits than the single measurement with the fewest significant
digits. In other words, the least precise single measurement determines the precision
of the final product or quotient.
Sample Problem 1.3.2 — Multiplication and Division
1. Multiply 2.54 cm × 5.08 cm.
2. Divide 56.8 m 2 by 2.3 m.
What to Think About
1. Multiplication
1. Determine uncertain digits. Indicated in bold.
2. Multiple with calculator.
3. Answer is not to correct number of significant digits.
4. Solve and report with correct number of digits after
decimal point. Remember to multiple units as well.
2. Division
1. Determine uncertain digits. Indicated in bold.
2. Divide with calculator.
3. Answer is not to correct number of significant digits.
4. Solve and report with correct number of digits after
decimal point. Remember to divide units as well.
How to Do It
2.54 cm × 5.08 cm
12.9032 cm 2
12.9 cm 2
56.8 m 2 by 2.3 m
24.695652
25 m
© Edvantage Interactive 2012 ISBN 978-0-9864778-3-6 Chapter 1 Skills, Methods, and the Nature of Physics 15