**Rounding off numbers**

To ’round off’ or ‘approximate’ a number to a desired degree of accuracy, we

- round the number
*up*if the next digit is 5 or more - round the number
*down*if the next digit is less than 5.

We represent approximately equal to as and approximately as ‘~’

**Examples**:

- 73 is close to 70 if approximating to or rounding in “tens”. So

73 ~ 70 (Read as 73 is approximately equal to 70)

- 86 is close to 90 when rounded off to the nearest “tens”, or approximate to the nearest “tens”

86 ~ 90

- 650 ~ 700 when rounded off to the nearest hundreds
- 26432 rounded off to
- nearest 100 is 264 /32 ~ 26400
- nearest 10,000 is 2 /6432 ~ 30000

**Strategy to round off numbers**

- Put a line where you want to round off. In the above example 3 to round off 650, put a big line after 6, because 6 is in the hundreds place and you want to round to the nearest hundred.

6/50

- The digit before the big line (6 in this case) will go up by 1, and the rest of the digits after the line will become 0, since the number after the line is 5. So the answer is 700.

**Estimation**

Estimating numbers

Example

A school has 21 classes. One of the second-year classes has 34 students. Estimate the number of students in the school.

First method

Round off the number to 1 s.f.

Number of classes ≅ 20

Number of students per class ≅ 30

Number of students in school ≅ 20 X 30

≅ 600

Second method

Assume the second-year class represents every class in the school.

Number of students in school

≅ 21 X 34

≅ 714

≅ 700 to 1 significant figure

Notice that there can be varying answers when estimating. In example 3, different methods give 600 to 700 students. However, both numbers are of the same order of size. Knowing that the school contains 600 to 700 students gives a good idea aof the size of the school. Thus, either number is a useful estimate.

Example

A student writes 47 words in five lines of writing. His exercise book has 28 lines on each page.

- Approximately how many words does he write on one page?
- How many pages will a 750-word essay take up?

Solution

- Five lines of writing contain 47 words.

One line of writing contains 47/5 ≅ 9 words.

28 lines of writing contain approximately 9 X 28 = 252 words.

Approximately 250 words are written on each page.

**Estimate quantities using traditional measures**

Market traders often use traditional measures to estimate quantities. For example, dry measures such a s rice, beans are sometimes measured in cups, basins and sacks.

Liquids such as palm oil, groundnut oil and kerosene are measured in jars, bottles and tins. Medicine is often measured in teaspoons.

**EXERCISES**

Lets see how much you’ve learnt, attach the following answers to the comment below

- 20 cups ≅ 1 basin, 20 basin ≅ 1 sack (a) A sack contains 100kg of rice. Estimate the number of kilograms of rice in 1 basin. Estimate the number of grams of rice in 1 cup. (b) A trader buys a sack of rice for N6, 000, she sells it as at N200 per basin. Estimate her profit on a sack of rice.
- A school has 27 classes. One of the classes has 33 students. Estimate the numbers of students in the school.
- A college has 689 students. The average mass of a student is approximately 51 kg. Estimate the total mass of all the students in the school.