Lesson 7, Topic 3
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# Rounding Off Numbers

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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.

Rules:

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

2. Round up digits  5, 6, 7, 8, 9   (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. 25.2999

to

i. 1 d.p
ii. 2 d.p
iii. 3 d.p

Solution a

i. 17.6536 to 1 d.p

5  is closest to 6 (the 1st d.p)

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

= 17.7

ii. 17.6536 to 2 d.p

3  is closest to 5 (the 2nd d.p)

3 is a round-down number so we add 0

= 17.65

iii. 17.6536 to 3 d.p

6  is closest to 3 (the 3rd d.p)

6 is a round-up number so we add 1

= 17.654

Solution b

i. 25.299 to 1 d.p

9  is closest to 2 (the 1st d.p)

9 is a round-up number so we add 1

= 25.3

ii. 25.299 to 2 d.p

9  is closest to 9 (the 2nd d.p)

9 is a round-up number so we add 1

= 25.30

iii. 25.299 to 3 d.p

9  is closest to 9 (the 3rd 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 1st decimal place etc.

Tenth =  1st d.p

Hundredth =  2nd d.p

Thousandth = 3rd d.p

Ten Thousandth = 4th d.p

Hundred Thousandth = 5th d.p

Millionth = 6th d.p

Ten Millionth = 7th d.p

Hundred Millionth = 8th d.p

Billionth =  9th d.p

### Example 2

Round of  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 = 1st 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 = 2nd 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 = 3rd 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 = 6th 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:

1. Express the following in standard form

a.    90785
b.    29560578
c.    287.251
d.    20000
e.    55000
f.    107000
g.    770
h.    4

2. Change these standard forms to ordinary numbers

a.    6.2 × 10o
b.    4.3 × 105
c.    9.37 × 107
d.    3.02 × 106
e.    1.2 × 103
f.    15.23 × 104

3. Express these numbers in standard form:

a.    0.546
b.    0.000307
c.    0.00275
d.    0.000 057
e.    0.000 0001
f.    0.251
g.    0.0251
h.    0.00251
i.    0.000251
j.    0.000 0251

4. Express the following as decimal fractions:

a.    4.3 x 10-3
b.    3.2 x 10-5
c.    1.89 x 10-7
d.    1.3 x 10-4
e.    3.08 x 10-2
f.    9 x 10-5
g.    4 x 10-6
h.    5.5 x 10-3

5. Round the following to

i.    1  d.p
ii.    2 d.p
iii.    3 d.p
iv.    4. d.p

a.    0.088055
b.    25.43998
c.    16.27092
d.    0.99905

6. Round off the following to the nearest

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

a.    5. 248 635 299
b.    3. 998 225 698

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