Express the following recurring decimal expansions in the form p/q, where p and q are integers and q ≠0 . i)0.5555

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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