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Society for Amateur Scientists

What are Significant Figures?

Significant figures are digits in a measurement that are reported because they are known with some certainty. The last digit -- the one farthest to the right -- is the one uncertain digit that is considered significant, even though it is estimated. Ask yourself how many places an instrument should be read before taking measurements and then record all the known digits plus an estimated digit. For example, a buret reading may be 27.61 mL. Because the markings on a buret are in tenths of a mL, the first three digits are known for certain. The final digit, 1, can only be estimated but still is considered significant. Confusion arises when zeros are involved. In our numbering system, zero is used not only as a number, but also as a place holder. When zero is used solely as a place holder, such as in 0.0034 g, the zeros are not significant. When zero is used as a number, such as 3.40 g, the zeros are significant. The trailing zero indicateds that the object had a mass of exactly 3.40 grams; not 3.39 grams or 3.41 grams. Thus, the zero at the end of the measurement to the right of the decimal point is significant. But what if an answer is 1400 grams? In this case, it is not certain if the final zeros are acting as numbers or place holders. To eliminate the ambiguity, the answer would be written as 1400. = 1.400*10³ if the zeros are significant or as 1400 = 1.4*10³ if the zeros are not significant.

Calculators do not check the number of significant figures so you will have to manually determine them. The basic rules are:

1. In addition or subtraction, the answer has the same number of decimal places as the number with the fewest decimal places. The number of significant figures in a sum can be greater than or the same as the numbers involved while the number of significant figures in a difference can be less than or the same as the numbers involved!

2. When multiplying or dividing, the answer has the same number of significant figures as the factor with the fest significant figures.

3. If a calculation involves non-linear functions, e.g. logarithms, special rules have to be used.

4. For calculations involving a combination of operations, you must check the number of significant figures in each portion of the calculation.

5. In a calculation involving multiple operations, do all the calculations before rounding off. Then return to the original numbers to decide where to round off a calculation.

6. Exact numbers such as "1 mole" and "1 km = 1000 m" have an infinite number of significant figures.

7. If you have to round a number where the first non-significant digit is a 5, round up only when it makes the final digit even. For example, 3.65 would round to 3.6 while 3.75 would round to 3.8.

If you wish to test yourself, solve the following problems.

What is the volume of 0.120 moles of an ideal gas at a pressure of 230 torr and a temperature of 20 Centigrade?

Volume = (0.120)(0.08206)(273.15+20)/(230/760)liters = 9.5 liters

What is the volume of 0.120 moles of an ideal gas at a pressure of 230. torr and a temperature of 20. Centigrade?

Volume = (0.120)(0.08206)(273.15+20.)/(230./760)liters = 9.53 liters

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