SIGNIFICANT DIGITS

SIGNIFICANT DIGITS

Significant Digits

Contrary to popular belief, the concept of significant digits was not developed to make life difficult for students. Unfortunately, we do not often do the subject justice in the classroom. The classroom is where you need to learn it so as to get you into the habit of displaying results to a proper degree of accuracy; not to much, not to little Click here to read a 'Significant Figures Fable'

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Significant Digits

Although the significant digits fable is fictitious, it is not unrealistic. As implied, the incorrect specification of a measurement can have dire consequences. At the very least, it implies a certain lack of knowledge on your part

Calculatoritis ? The dreaded disease that forces you to write every digit displayed by your calculator regardless of how it was obtained

Hopefully, the next few pages will make it apparent the answer displayed by the calculator is not the answer you should necessarily record. Your calculator can be set to display any number of desired decimal points...it cannot be set to display significant digits. You must do that!

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Rules of Significant Digits

It is important to determine the number of significant digits for any measurement or calculation. The following are basic rules of significant figures

Non-zero digits are always significant

Any zeros between two significant digits are significant

A final zero or trailing zeros in the decimal portion ONLY

are significant

The table to the right provides a number of examples

Number 1002.03 0.00405 2500

Significant Digits 6 3 2

2500.

4

2500.0

5

0.034 x 10-7

2

1.034 x 10-7

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Exact Numbers vs Measurements

The concept of significant digits is applicable only to measurements, not to definitions. For example, if you measure the length of a steel rod and express that length as 23.275 cm, this implies the accuracy of the measurement is ?0.0005 cm. You are also expressing this measurement to 5 significant digits

On the other hand, we know there are exactly 12 inches in one foot. This is a definition, not a measurement. In this case, the number 12 has an infinite number of significant digits. If used in a calculation, it has no impact on the number of significant digits to which you display the answer

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