Significant Figures
Part II: Calculations
Objectives
• When you complete this presentation, you will
be able to
– determine the number of significant figures in a
calculated answer
Introduction
• We know how to determine the number of
significant figures in a measurement.
– 3.442 g has 4 significant figures
– 0.0025 m has 2 significant figures
– 140 s has 2 significant figures
– 0.000420 mL has 3 significant figures
• Now, we need to learn how to use those
measurements in calculations.
Rounding
• In general, a calculated answer cannot be
more precise than the least precise
measurement from which it was calculated.
• The calculated value must be rounded to
make it consistent with the measurements.
Rounding
• To round, we need to determine how many
significant figures the answer needs to have.
– This depends on the measurements and the math
process used to determine the answer.
– We will cover the details of that later in the
presentation.
• First, let’s practice rounding numbers to a
proper number of significant figures.
Rounding
• How do we round a numerical value?
• We use the same rules we have always used.
– If the digit to the immediately to the right of the
last significant digit is less than 5, we drop the rest
of the digits and the value of the last significant
digit remains the same.
Round 45.244 to 3 sig figs ➠ 45.244 ➠ 45.2
Round 0.85321 to 2 sig figs ➠ 0.85321 ➠ 0.85
Rounding
• How do we round a numerical value?
• We use the same rules we have always used.
– If the digit to the immediately to the right of the
last significant digit is 5 or greater we drop the
rest of the digits and the value of the last
significant digit is increased by 1.
Round 62.557 to 3 sig figs ➠ 62.557 ➠ 62.6
Round 0.0545 to 2 sig figs ➠ 0.0545 ➠ 0.055
Rounding
Example 1: Round each of the following numbers to
the indicated number of significant figures:
1. 54,525.99 m to 3 sig figs
54,500 m
0.007146 kg
2. 0.00741554 kg to 4 sig figs
40 s
3. 37.255 s to 1 sig fig
0.78 cm
4. 0.78245 cm to 2 sig figs
360,000 km
5. 355,000 km to 2 sig figs
0.0383 L
6. 0.0382574925 L to 3 sig figs
Calculations – addition and subtraction
• The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of
decimal places.
• For example:
12.52 m
The 349.0 m measurement has the
least number of decimal places.
+ 349.0 m
+ 8.24 m
369.76 m
Calculations – addition and subtraction
• The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of
decimal places.
• For example:
12.52 m
That measurement will control the
number of decimal places in the
answer.
+ 349.0 m
+ 8.24 m
369.76 m
Calculations – addition and subtraction
• The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of
decimal places.
• For example:
12.52 m
The reported answer should be
369.8 m
+ 349.0 m
+ 8.24 m
369.76 m
Calculations – addition and subtraction
Example 2: Perform each operation. Express the
answer in the correct number of sig figs.
79.2 m
1. 61.2 m + 9.35 m + 8.6 m
23.8 g
2. 14.2 g + 8.73 g + 0.912 g
109 s
3. 35 s + 72.1 s + 1.876 s
7.33 kg
4. 9.44 kg – 2.11 kg
11.53 cm
5. 1.36 cm + 10.17 cm
17.3 mL
6. 34.61 mL – 17.3 mL
Calculations – multiplication and division
• The answer to a multiplication or division
calculation should be rounded to the same
number of significant digits as the
measurement with the least number of
significant digits.
• For example:
7.55 m
× 0.34 m
The 0.34 m measurement has the
least number of significant digits (2).
2.567 m2
Calculations – multiplication and division
• The answer to a multiplication or division
calculation should be rounded to the same
number of significant digits as the
measurement with the least number of
significant digits.
• For example:
7.55 m
That measurement will control the
number of decimal places in the
answer.
×
0.34 m
2.567 m2
Calculations – multiplication and division
• The answer to a multiplication or division
calculation should be rounded to the same
number of significant digits as the
measurement with the least number of
significant digits.
• For example:
7.55 m
The reported answer should be
2.6 m2
×
0.34 m
2.567 m2
Calculations – multiplication and division
Example 3: Perform each operation. Express the
answer in the correct number of sig figs.
1.5 m2
1. 2.10 m × 0.70 m
0.29 kg
2. 2.4526 kg ÷ 8.4
18 m2
3. 8.3 m × 2.22 m
675 kg
4. 8432 kg ÷ 12.5
480 s
5. 32 s × 15.125
2.00 mL
6. 34.61 mL ÷ 17.3
Summary
• A calculated answer cannot be more precise
than the least precise measurement from
which it was calculated.
• The calculated value must be rounded to
make it consistent with the measurements.
Summary
• Rules for rounding:
– If the digit to the immediately to the right of the
last significant digit is less than 5, we drop the rest
of the digits and the value of the last significant
digit remains the same.
– If the digit to the immediately to the right of the
last significant digit is 5 or greater we drop the
rest of the digits and the value of the last
significant digit is increased by 1.
Summary
• Significant figures in calculations:
– The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of decimal
places.
– The answer to a multiplication or division
calculation should be rounded to the same
number of significant digits as the measurement
with the least number of significant digits.