Question

express 0.6+0.7+0.bar47 in the form of p/q where p and q are integers and q is not equal to 0

Answer 1

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Solution :-

Let x = 0.7Bar

⇒ x = 0.777.......... .........(1)

Multiplying (1) by 10

⇒ 10x = 7.7...... = 7.777 ...........(2)

Subtracting (1) from (2)

⇒ 10x - x = 9x

⇒ 7.777 - 0.777 = 7

⇒ 9x = 7

⇒ x = 7/9

Let y = 0.47Bar

⇒ y = 0.4747 .............. ........(1)

Multiplying (1) by 100

⇒ 100y = 47.4747 ............(2)

Subtracting (1) from (2)

⇒ 100y - y = 99y

⇒ 47.4747 - 0.4747 = 47

⇒ 99y = 47

⇒ y = 47/99

Now,

0.7Bar = 7/9

and 0.47Bar = 47/99

0.6 = 6/10

6/10 + 7/9 + 47/99

Taking L.C.M. of the denominator and then solving it, we get.

⇒ (594 + 770 + 470)/990

⇒ 1834/990

⇒ 917/495________answer

Hence, 0.6 + 0.7Bar + 0.47Bar = 917/495

I think my answer is capable to clear your confusion

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Answer 2

Answer:

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