There are instances where laboratory calculations must be applied to two or more measured values with a differing number of significant figures.
The two main rules when determining the number of significant figures in a final calculation are grouped into addition & subtraction and multiplication & division sets.
- When adding or subtracting two or more measured values, the calculated result should have the resulting value that will have the same number of decimal places as the measured value with the fewest number of decimal places.
- This measured value with the fewest number of decimal places is also called the limiting value.
- An example is the addition of 36.948 and 41.02, creating the calculated value of 77.968. However, the limiting value in the original calculation is 41.02 which has 2 places after the decimal, meaning the final calculated result needs to be rounded at the hundredth place (2 places after the decimal) or 77.97.
- Note that the rounding occurs after the addition or subtraction of the original numbers.
- When multiplying or dividing two or more measured values, the calculated result should have the resulting value that will have the same number of significant figures as the value with the fewest number of significant figures.
- An example is the division of 9.75513 and 2.31, creating the calculated value of 4.223. However, the measured value with the fewest number of significant figures is 2.31 with 3 significant figures, meaning the final calculated result needs to be rounded at the hundredth place (to make a calculated value with 3 calculated figures) or 4.22.
- Note that the rounding occurs after the multiplication or division of the original numbers.
- Order of operations using PEMDAS still applies.
Here are examples of calculations where the number of significant figures in each measured value must be considered to complete the resulting calculation with the correct number of significant figures.
- 38.65 + 20.103 = 58.753 (calculated value) = 58.75 (rounded value)
- 2,350.75 – 92.3 = 2,258.45 (calculated value) = 2,258.4 (rounded value)
- 0.1120 x 130 x 2,800. = 40,768 = 41,000
- 5.055 / 0.0044 = 1,148.863636 = 1,100
