Transcript Slideshow

How to Multiply and Divide Numbers that
Have Significant Figures
Introduction
• Measurements are always approximations to a true value. There
will always be some level of uncertainty in a measurement. The
uncertainty in a measurement is captured by the number of
significant figures used to express it.
• We must be mindful of the number of significant figures in a
measurement so that when we work with these numbers we are
aware of how it has affected our final answer.
• For example, an edge of a square is measured to be 2.54 cm. Its
area is calculated to be 6.4516 cm2 using a calculator. This result is
absurd. Why? A more reasonable answer would be 6.45 cm2.
2
Rule for Multiplying and Dividing
When multiplying and dividing, the number of significant figures in each
of the numbers involved the operation determines how many significant
figures are in the final answer.
Rule when Multiplying and Dividing Numbers:
• Perform the indicated operation.
• Round the answer so that it has the same number of significant
figures as the number in the calculation that had the fewest
significant figures.
How to Round Off Numbers
Whether to round up or down is based on if the
amount dropped is greater than or less than one-half
the value of the last digit retained.
Rules
Examples
Round up if the amount dropped is greater than
one-half the value of the last digit retained.
2.376 becomes 2.38
93.8 becomes 94.
0.126 becomes 0.13
Round down if the amount dropped is less than
one-half the value of the last digit retained.
2.374 becomes 2.37
93.3 becomes 93.
0.121 becomes 0.12
If the amount dropped is exactly one-half the value
of the last digit retained, then round so that the last
digit retained is even.
2.375 becomes 2.38
93.5 becomes 94.
0.125 becomes 0.12
Examples
3.86
x 0.4
1.544
2.
[3 sig. figs.]
[1 sig. fig.]
[1 sig. fig.]
Examples
12.44 [4 sig. figs.]
x 6.27 [3 sig. fig.]
77.9988
78.0
[3 sig. figs.]
Examples
8.15
[3 sig. figs.]
÷ 3.2
[2 sig. figs.]
2.546875
2.5
[2 sig. figs.]
Examples
0.756
÷ 0.16
4.725
4.7
[3 sig. figs.]
[2 sig. figs.]
[2 sig. figs.]
Examples
(2.047)2 [4 sig. figs.]
4.190209
4.190
[4 sig. figs.]
Problems
1) 2.93 x 4.5 =
2) 94.03 x 317.76 =
3) 0.3804 x 4.83 =
4) 8.28 ÷ 3.2 =
5) 1.40 ÷ 2.342 =
6) 2.941 ÷ 0.0250 =
Problems - Key
1) 2.93 x 4.5 = 13.
2) 94.03 x 317.76 = 29880
3) 0.3804 x 4.83 = 1.84
4) 8.28 ÷ 3.2 = 2.6
5) 1.40 ÷ 2.342 = 0.598
6) 2.941 ÷ 0.0250 = 118.