Express 0.6 +0.7 bar as a rational number in the form of p/q,where p,q€ z and q ≠0
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bro this answer will be
pqz =1.3
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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
nd 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
Hence, 0.6 + 0.7Bar + 0.47Bar = 917/495
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