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 Calculations using Significant Figures

Your calculated value cannot be more precise than the least precise quantity used in the calculation. The least precise quantity has the fewest digits to the right of the decimal point. Your calculated value will have the same number of digits to the right of the decimal point as that of the least precise quantity.

Example
32.01 m
5.325 m
12 m

Added together, you will get 49.335 m, but the sum should be reported as '49' meters.

 Example #1                                2.311 Example #2                                37.438 -2.11 -6.50 Answer not rounded--> 0.201 Answer not rounded--> 30.938 Rounded to least number of decimal places--> 0.20 Rounded to least number of decimal places--> 30.94

Multiplication and Division

The number of significant figures in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation.

ex.

 15 ÷ 3.155= 4.754358 ==>4.8 2s.f. 4.s.f. so this will have 2 s.f.

 5.60 x 7.102= 39.7712 ==>39.8 3 s.f. 4.s.f. so this will have 3 s.f.

Advanced Significant Figure Calculations ***Combined Operations

Remember to follow the order of operations. Be sure to remember to include only the sig. figs. before going on to the next operation.

Losing Significant Figures

Sometimes significant figures are 'lost' while performing calculations. For example, if you find the mass of a beaker to be 53.110 g, add water to the beaker and find the mass of the beaker plus water to be 53.987 g, the mass of the water is

53.987-53.110 g = 0.877 g

The final value only has three significant figures, even though each mass measurement contained 5 significant figures.

Rounding and Truncating Numbers

There are different methods which may be used to round numbers. The usual method is to round numbers with digits less than '5' down and numbers with digits greater than '5' up (some people round exactly '5' up and some round it down).

Example:
If you are subtracting 7.799 g - 6.25 g your calculation would yield 1.549 g. This number would be rounded to 1.55 g, because the digit '9' is greater than '5'.

In some instances numbers are truncated, or cut short, rather than rounded to obtain appropriate significant figures. In the example above, 1.549 g could have been truncated to 1.54 g.

Exact Numbers

Sometimes numbers used in a calculation are exact rather than approximate. This is true when using defined quantities, including many conversion factors, and when using pure numbers. Pure or defined numbers do not affect the accuracy of a calculation. You may think of them as having an infinite number of significant figures. Pure numbers are easy to spot, because they have no units. Defined values or conversion factors, like measured values, may have units. Practice identifying them!

Example:
You want to calculate the average height of three plants and measure the following heights: 30.1 cm, 25.2 cm, 31.3 cm; with an average height of (30.1 + 25.2 + 31.3)/3 = 86.6/3 = 28.87 = 28.9 cm. There are three significant figures in the heights; even though you are dividing the sum by a single digit, the three significant figures should be retained in the calculation.

Practice Problems

 Problems Highlight to reveal answers 7846 X 92437  X 235.649 X 3300= 560000000000000   or 5.6 X 1014 583.00 ÷ 83= 7.0 (57.6 X 3) ÷ (34 X 3.00 X 87.507)= 0.02 78.00 + 45.6 + 0.00467 + 39.45 + 276.999= 440.1 567.000 - 12= 555 8597 - 0.l= 8597 (3.50 X 105)  X [2.8 ÷ (5.4  - 4.09)]= 750000 (6.10 X 107 ) + (3 X 107 )= 9 X 107 787  X 3.0= 2400