Question

Write 0.123 bar in the form of q is not equal to 0

Answer 1

Q. Write 0.123 (bar on 123) in the form p/q in which p and q are integers and q ≠ 0.

Solution :

Let

x = 0.123123123................. (i)

1000x = 123.123123........... (ii)

(ii) - (i) = 123.123123... - 0.123123...

1000x - x = 123

999x = 123

x = 123/999

Hence,
0.123( bar on 123) = 123/999 (in p/q form)

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Q. Write 0.123 (bar on 23) in the form p/q in which p and q are integers and q ≠ 0.

Solution :

Let

10x = 1.232323................. (i)

1000x = 123.2323........... (ii)

(ii) - (i) = 123.2323... - 1.2323...

1000x - 10x = 122

990x = 122

x = 122/990

Hence,
0.123( bar on 23) = 122/990 (in p/q form)

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Q. Write 0.123 (bar on 3) in the form p/q in which p and q are integers and q ≠ 0.

Solution :

Let

100x = 12.333333................. (i)

1000x = 123.33333........... (ii)

(ii) - (i) = 123.333... - 12.333...

1000x - 100x = 111

900x = 111

x = 111/900

Hence,
0.123( bar on 3) = 111/900 (in p/q form)