| Contents for this page | Related topics |  |
|
Significant figures Rounding off a number Additional questions |
Dimensions Scientific notation Units and measurements |
 Data
|
| Learning Outcomes | ||
| After studying this section, you will (a) understand the concept of significant figures and (b) be able to round off numbers to a given number of significant figures. | ||
Numbers which are the result of an observation or measurement (measures) are approximations, and are subject to error. The precision of the measurement should be reflected by writing down only those figures in which the observer has confidence.
The confidence of the observer is reflected in the number of significant figures used to write down the number.
For example, the quantity 1.23 metres is expressed here to 3 significant figures, implying that there is some uncertainty in the last (rightmost) digit. We know that the number is in the range 1.225 to 1.234 (all numbers in the range 1.225 to 1.234 would be rounded off to 1.23).
Integers (whole numbers) are considered to have an infinite number of significant figures.
For decimal fractions, leading zeros (zeros to the left of the first non-zero digit) are not considered to be significant figures, but trailing zeros (to the right of the last non-zero digit) are:
0.0123 has 3 significant figures
0.4560 has 4 significant figures.
Numbers which are written as whole numbers with trailing zeros (i.e., 1000, 102300) present a problem. The number of significant figures should be seen in context, but generally, the trailing zeros of such numbers are not considered to be significant figures.
For example, 1000 has 1 significant figure, unless it is clear that it is an exact number (resulting from an accurate count, for example).
If you want to express precision to four significant figures of a number subject to an error, use exponential notation:
1.000 x 103 has 4 significant figures.
2 x 10-2 has 1 significant figure.
| After adding or subtracting numbers, you should round off your answer in such a way as to retain digits as far as the first column in which there is uncertainty: |  |
 |
The result of a multiplication or division should be rounded off to as many significant figures as the least exact factor. |
Glossary