To round off numbers simply means making a number simpler but keeping its value close to what it was. Rounding numbers means adjusting the digits (up or down) to make rough calculations easier.

The result will be an estimated answer, not a precise one.

For example, if the population of a country is 8, 214, 426 in a certain year, this number is hard to remember but if we say the population of that country is 8 million, it is a good estimate, because it does not make any real difference what the exact number is.Â For example, 73 is rounded off to 70 because 73 is closer to 70 than 80.

**Rules:**

1. Round down digits 0, 1, 2,3,4, (i.e. add 0)

2. Round up digitsÂ 5, 6, 7, 8, 9 Â (i.e add 1)

To find the number of decimal places, simply count the number of figures after the decimal point.

**Decimal places (d.p)**

Example 1

Write

**a.** 17.6536

**b.** 25.2999Â

to

**i.** 1 d.p

**ii. **2 d.p

**iii.** 3 d.p

**Solution** **a**

**i.** 17.6536 to 1 d.p

1 d.p | 2 d.p | 3 d.p | 4 d.p | |||

1 | 7 | . | 6 | 5 | 3 | 6 |

5 is closest to 6 (the 1^{st} d.p)

5 is a round up number so we add 1 to 6

= 17.7

**ii.** 17.6536 to 2 d.p

1d.p | 2d.p | 3d.p | 4d.p | |||

1 | 7 | . | 6 | 5 | 3 | 6 |

3 is closest to 5 (the 2^{nd} d.p)

3 is a round down number so we add 0

= 17.65

**iii.** 17.6536 to 3 d.p

1d.p | 2d.p | 3d.p | 4d.p | |||

1 | 7 | . | 6 | 5 | 3 | 6 |

6 is closest to 3 (the 3^{rd} d.p)

6 is a round up number so we add 1

= 17.654

**Solution b**

**i.** 25.299 to 1 d.p

1d.p | 2d.p | 3d.p | 4 d.p | |||

2 | 5 | . | 2 | 9 | 9 | 9 |

9 is closest to 2 (the 1^{st} d.p)

9 is a round up number so we add 1

= 25.3

**ii.** 25.299 to 2 d.p

1d.p | 2d.p | 3d.p | 4 d.p | |||

2 | 5 | . | 2 | 9 | 9 | 9 |

9 is closest to 9 (the 2^{nd} d.p)

9 is a round up number so we add 1

= 25.30

**iii. **25.299 to 3 d.p

1d.p | 2d.p | 3d.p | 4 d.p | |||

2 | 5 | . | 2 | 9 | 9 | 9 |

9 is closest to 9 (the 3^{rd} d.p)

9 is a round up number so we add 1

= 25.300

To round a decimal number to the nearest tenth (t) is the same as rounding to the 1^{st} decimal place etc.

Tenth = 1^{st} d.p

Hundredth = 2^{nd} d.p

Thousandth = 3^{rd} d.p

Ten Thousandth = 4^{th} d.p

Hundred Thousandth = 5^{th} d.p

Millionth = 6^{th} d.p

Ten Millionth = 7^{th} d.p

Hundred Millionth = 8^{th} d.p

Billionth =Â 9^{th} d.p

Example 2

Round ofÂ 62. 57498992Â to the nearestÂ

**i.** tenthÂ Â

**ii.** hundredthÂ

**iii.** thousandth

**iv.** millionth

**Solution**

**i.** 62. 57498992Â to the nearestÂ tenth

7 is closest to 5 (the Tenth = 1^{st} d.p)

7 is a round up number so we add 1

= 62.6 to the nearest tenth

**ii.** 62. 57498992Â to the nearestÂ hundredth

7 is closest to 4 (Hundredth = 2^{nd} d.p)

4 is a round down number so we add 0

= 62.57 to the nearest hundredth

**iii.** 62. 57498992Â to the nearestÂ thousandth

9 is closest to 4 (Thousandth = 3^{rd} d.p)

9 is a round up number so we add 1

= 62. 575 to the nearest thousandth

**iv.** 62. 57498992Â to the nearestÂ millionth

9 is closest to 9 (Millionth = 6^{th} d.p)

9 is a round up number so we add 1 which gives 10. In this case, we then add 1 to the column on the left which is 8.

= 62.574 990 to the nearest millionth.