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 **3****9**7.2, 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).

ExampleAnswerCalculate 3.185 x 8.693

Estimate: 3 x 9 = 27

Make an estimate first.

Accurate (from calculator): 27.687205