Just follow the steps below carefully. Say you need to find the value of 0.5555……
Step 1: Let x be the value of the repeating decimal which you are converting to p/q form
x = 0.5555……
We know the repeating digit is 5
Step 2: Multiply x by a power of 10, such that the resultant has same repeating digits on the right side of decimal. In this case if we multiply 10 both side, we get –
10x = 5.55555…….
Step 3: Subtract output of step 2 from step 1
10x – x = 5.555555……. – 0.555555…….
9x = 5
x = 5/9
Hence we have converted decimal into p/q form, where p and q are integers and q ≠0
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Written on May 24, 2019, 1:46 a.m.