Measurements always have some limitation on their precision. When you do
calculations with measurements (which you will undoubtedly have to do) the
results will need to reflect the limitations of the measurments upon which
they are based. The results will have their precision
limited by the precision of the least precise measurement. The measurement
with the smallest number of significant figures is the least precise
measurement. A result calculated based on that measurement cannot have higher
precision than the measurement you started with. Put another way: a chain is
only as strong as the weakest link. A relay race team is only as fast as its
slowest member.
Calculation Steps
Determine the number with the smallest number of significant figures to the right of the decimal point. The digits to the left of the decimal point do not contribute to determing the number of significant digits in the answer.
Add and subtract all numbers using all available digits.
Round the answer so that the decimal portion has the same number of digits as that in the number determined in step one.
Example:
5.67 + 27.893 + 4.3
‘4.3’ has the fewest number of digits after the decimal point
5.67
27.893
+ 4.3
——————
37.863 37.9 is the correct answer
Exercises
Perform the following calculations. Report answers with the correct number of significant figures and enter calculations into your calculator in such a way as to avoid rounding errors. Show all work, including units, at every step. Write neatly and do your work on another sheet of paper before recording your work and answers here.
Note: some problems have numbers expressed in different units. Be sure to convert all numbers to the same units before adding or subtracting.
4.5 cm + 6.78 cm
Calculator’s answer:
Correct answer:
No. of s.f.:
6.84 mm + 34 mm
Calculator’s answer:
Correct answer:
No. of s.f.:
4.938 m + 5.9 m + 6.78 m
Calculator’s answer:
Correct answer:
No. of s.f.:
8.95 km – 6.79 km
Calculator’s answer:
Correct answer:
No. of s.f.:
270.0 cm – 1.24 m
Calculator’s answer:
Correct answer:
No. of s.f.:
4.00 m3 + 120.0 L
Calculator’s answer:
Correct answer:
No. of s.f.:
14 mg + 0.0197 g
Calculator’s answer:
Correct answer:
No. of s.f.:
42.0 cm – 69.0 mm
Calculator’s answer:
Correct answer:
No. of s.f.: