# Express 0.6+0.7¯+0.47¯ in the form pq, where p and q are integers and q ≠ 0. - Mathematics

Sum

Express 0.6 + 0.bar7 + 0.4bar7 in the form p/q, where p and q are integers and q ≠ 0.

#### Solution

Let x = 0.6

Multiply by 10 on L.H.S and R.H.S,

10x = 6

x = 6/10

x = 3/5

So, the p/q form of 0.6 = 3/5

Let y = 0.77777…

Multiply by 10 on L.H.S and R.H.S,

10y = 7.7777…

10y – y = 7.7777777……. – 0.7777777…………..

9y = 7

y = 7/9

So the p/q form of 0.7777… = 7/9

Let z = 0.47777…

Multiply by 10 on L.H.S and R.H.S,

10z = 4.7777…

10z – z = 4.7777777… – 0.47777777…

9z = 4.2999

z = 4.3/9

z = 43/90

So the p/q form of 0.4777… = 43/90

Therefore, p/q form of 0.6 + 0.bar7 + 0.4bar7 is,

x + y + z = 3/5 + 7/9 + 43/90

= (54 + 70 + 43)/90

= 167/90

Concept: Real Numbers and Their Decimal Expansions
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#### APPEARS IN

NCERT Mathematics Exemplar Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 1 | Page 12

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