Rounding Off Numbers

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. For example, 73 is rounded off to 70 because 73 is closer to 70 than 80.

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

Decimal places (d.p)

Worked Example 7.3.1:

Write:

a. 17.6536
b. 25.2999 

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 =  9^th d.p

Worked Example 7.3.2:

Round off 62. 57498992  to the nearest:

i. tenth   
ii. hundredth 
iii. thousandth
iv. millionth

Solution

i. 62. 57498992  to the nearest 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. 57498992  to the nearest 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. 57498992  to the nearest 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. 57498992  to the nearest 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.

Evaluation Questions: