Question

Express each repeating decimal as a fraction. 0.6, 0.12, 0.82. Note: there is supposed to be a line over 6, 2, and 82

Answer 1

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is it 0.6 ????

Answer 2

yes

Answer 3

are u supposed to show the working or give answer by shortcut

Answer 4

I just dont know how to do it. Can you show the work on one and answer the rest so I can check them?

Answer 5

since there is only one digit repeating here (6) so our aim is to get one 6 before decimal point.
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Let p = 0.6 (= 0.6666---- (this goes on endlessly) ---- (1)
now to get one 6 before the decimal point multiply both sides by 10
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10p = 6.6 (= 6.666------ ) -------(2)
Subtract (1) from (2)
- -
10p - p = 6.6 - 0.6
9p = 6
p = 6/9
p = 2/3
- 2
so 0.6 = -----
3

Answer 6

got it?????

Answer 7

got it. so what is 0.12...2 repeating and 0.82...8and2 repeating

Answer 8

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now we come to 0.12 (= 0.1222222-------)

Here we find that before the repeating digit 2, there is one non-repeating digit i.e.1
so we have to first bring this 1 before the decimal and then 2 once before the decimal point. we proceed as follows:
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Let p = 0.12 ------(1)
Multiply both sides of (1) by 10
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10p = 1.2 ------(2)

Now multiply both sides of (1) by 100
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100p = 12.2 ------(3)

subtract (2) from (3)
- -
100p - 10p = 12.2 - 1.2
90p = 11
p = 11/90

- 11
so 0.12 = ------
90

Answer 9

got it????

Answer 10

got it and what is just the answer for 0.82

Answer 11

--
0.82 (= 0.828282.......)
Here we have two repeating digits so we have to get one pair of 82 before the decimal point..
--
Let p = 0.82 ------------- (1)
multiply both sides of (1) by 100
--
100p = 82.82 -----------(2)

subtracting (1) from (2)

-- --
100p - p = 82 .82 - 0.82

99p = 82
p = 82/99
-- 82
so 0.82 = -------
99

Answer 12

is the concept/method clear now???

Answer 13

yes thank u!

Answer 14

u r welcome :))
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