Approximation methods
15.79 is 16 to the nearest whole number.
3,125 is 3,200 to the nearest hundred.
Two special approximation methods are used in mathematics: decimal places (d.p.) and significant figures (s.f.).
Significant figures (s.f.)
All figures are counted except zeros between the decimal point and the first non-zero digit, and place-value zeros before the point.
Example:
126.87 is 130 to two s.f. (zero is not a significant figure, but is needed to show the empty units columns, otherwise 126.87 would be 13, which is silly).
Example:
0.00134 is 0.0013 to two s.f.
Example:
0.0598 is 0.060 to two s.f.
The most significant figure in a number is the first non-zero digit that you reach when reading a number from left to right. In the following examples, the most significant figure is shown in red: 4568, 75007, 89, 0.03668, 0.00533, 3.14.
Remember:
-
if the key digit is less than 5 round down
-
if the key digit is greater than 5, or if it is a five followed by digits other than zero, round up
When approximating to a stated number of significant figures, the rules for rounding are used on the last significant figure as in the following chart:
| given number |
number of significant figure |
key digit |
rounded number |
| 7462 |
two |
7462 |
7500 |
| 0.004207 |
one |
0.004207 |
0.004 |
| 3562.14 |
three |
3562.14 |
3560 |
| 0.25437896 |
four |
0.25437896 |
0.2544 |
| 0.565 |
one |
0.565 |
0.6 |
Rounding to a required place value or to a given number of significant figures depends upon the application and what is required in the question.
Exercise 1
Round off the value 69.846525 to:
| a) |
3 significant figures |
| b) |
2 significant figures |
| c) |
5 significant figures |
| d) |
7 significant figures |
| e) |
4 significant figures |
| f) |
6 significant figures |
Solution:
|
