Calculations with Significant Figures
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Transcript Calculations with Significant Figures
Sig Figs meet Rounding!
In Science we take measurements, but those
measurements are sometimes needed to find the
values that we really want.
For example:
Volume (Length x Width x Height)
Volume by Difference using a graduated cylinder
(Height of Water with object – Height of water initially)
Density (Mass ÷ Volume)
Calculations cannot be more precise than the
measurements.
The least precise measurement dictates the precision
of the answer
The least precise will be the measurement with the
LEAST decimal places.
When adding or subtracting – pretend that you are
back in elementary school and line those numbers up!
Example: Two different pieces of metal are massed
separately using different balances. The first piece has
a mass of 19.473 g. The second piece has a mass of 3.82
g. What is the total mass? Don’t forget to use
significant figures.
Step 1 – Line them up and do the math.
19.473
+ 3.82
23.293
Step 2 – Find the LAST significant figure. Start from
the right. Look for the first column that has a
significant figure from both measurements. Underline
the number in the answer that is in that column.
19.473
+ 3.82
23.293
Step 3 – Round to that place – do not forget to LOOK
right!
19.473
+ 3.82
23.293
Answer : 23.29 g – Don’t forget the Unit!!!
Subtraction is the SAME!!!
Example – The mass of a paper cup is 1.284 g. The
mass of the paper cup plus a sample of Manmium is
38.2 g. What is the mass of the Manmium sample?
Step 1 – What is it?
Yep – Line them up!
38.2
- 1.284
36.916
Step 2 – What is it?
Yep – Underline the last significant figure!
38.2
- 1.284
36.916
Step 3 – What is it?
Yep – Look right and ROUND!
38.2
- 1.284
36.916
Answer = 36.9 g
489.2 g + 8.03 g = ?
0.2800 L + 4.8 L =?
285.0 kg – 3.82 kg = ?
0.01963 g + 0.290 g =?
926.028 kg – 30.02 kg = ?
3902 L + 284.5 L = ?
489.2 g + 8.03 g = 497.2 g
0.2800 L + 4.8 L = 5.1 L
285.0 kg – 3.82 kg = 281.2 kg
0.01963 g + 0.290 g = 0.310 g
926.028 kg – 30.02 kg = 896.01 kg
3,902 L + 284.5 L = 4,186 L
The least precise measurement dictates the precision
of the answer
The least precise will be the measurement with the
LEAST number of significant figures.
The answer should be rounded to the least number of
significant figures
Example: Find the area of a rectangle with a length of
24.35 m and a width of 4.09 m.
Step 1 – Do the math!
Area = Length x width
24.35 m x 4.09 m = 99.5915 m2
Step 2 – Determine the number of significant figures
in the original measurements
24.35 m (4 sig figs)
4.09 m (3 sig figs)
Step 3 – Determine the least number of sig figs
3 sig figs is less than 4 sig figs
Step 4 – round the answer to the least number of sig
figs that you determined in Step 3
99.5915 m2
Final Answer – 99.6 m2
Division is the same!
Example – An object has a mass of 48.309 g and a
volume of 9.28 mL. What is the density of this object?
What is Step 1?
Yep – do the math!
Density = mass/volume
Density = 48.309 ÷ 9.28 = 5.20571121 g/mL
What is Step 2?
Yep – determine the number of significant figures in
each of the original measurements
48.309 g (5 sig figs)
9.28 mL ( 3 sig figs)
What is Step 3?
Yep – determine the least number of sig figs in the
original measurements
3 sig figs
What is Step 4?
Yep – Round to the least number of sig figs found in
Step 3
5.20571121 g/mL round to three sig figs
Final Answer = 5.21 g/mL
40.38 cm x 3.2903 cm = ?
0.00382 m x 0.08291 m = ?
293.0 g ÷ 3.0023 cm3 = ?
3.0193 x 104 kg ÷ 4.93 L = ?
293.0 cm x 3.28 cm = ?
Challenge: 3.927 cm x 12.736 cm x 4.000 cm = ?
40.38 cm x 3.2903 cm = 132.9 cm2
0.00382 m x 0.08291 m = 0.000317 m2 or 3.17 x 10-4 m2
293.0 g ÷ 3.0023 cm3 = 97.59 g/cm3
3.0193 x 104 kg ÷ 4.93 L = 6,120 kg/L or 6.12 x 103 kg/L
293.0 cm x 3.28 cm = 89.3 cm2
Challenge: 3.927 cm x 12.736 cm x 4.000 cm = 200.1 cm3