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Question

Show that 1.¯¯¯¯¯¯34 can be expressed in the form pq, where p and q are integers and qo.

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Solution

Let the given number be,
x=1.¯34

x=1.34343434........(i)

On multiplying 100 on both sides, we get:
100x=134.343434.......(ii)

Subtracting (i) from (ii), we get:

100xx=134.343434...1.343434...=133

99x=133

x=13399

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