When making calculations or taking measurements, approximations have to be made. Numbers can be approximated to a certain number of decimal places (often called dec. pl. or d.p.) or significant figures (often called sig.fig. or s.f.). Both methods involve the process of 'rounding off'.
Significant Figures
In any number, the first non-zero digit is the first significant digit, the next digit is the second significant digit, etc.
e.g. In the number 397.2, the first significant digit is 3 and the second significant digit is 9.
When approximating a number to a given number of significant figures:
- Begin with the first non-zero digit and count in the number of significant figures required.
- Then, if the next digit is a 5 or above, add 1 on to the last significant digit.
- If it is below a 5, leave it as it is. This process is known as 'rounding off '.
| e.g. | 325.6 | (to 3 significant figures) | 326 |
| 0.045 | (to 1 significant figure) | 0.05 | |
| 72.9 | (to 2 significant figures) | 73 | |
| 821 | (to 1 significant figure) | 800 |
Decimal Places
When writing a number to a given number of decimal places:
- Begin by counting in the digits from the decimal point.
- Then, if the next digit is a 5 or above, add 1 on to the last digit.
- If the next digit is below a 5, leave it as it is.
| e.g. | 7.32 | (to 1 decimal place) | 7.3 |
| 0.058 | (to 2 decimal places) | 0.06 | |
| 4.6398 | (to 3 decimal places) | 4.640 | |
| 51.69 | (to 1 decimal place) | 51.7 |
Estimation
Before making a calculation or solving a problem, especially when using a calculator, an approximate answer should be obtained. This process helps to eliminate mistakes from incorrect keying and calculator malfunction.
Estimates can be obtained mentally by approximating the numbers in the calculation to 1 or 2 significant figures (depending on the question).
Example Answer Calculate 3.185 x 8.693
Estimate: 3 x 9 = 27
Make an estimate first.
Accurate (from calculator): 27.687205
