Question

Express each of the following in the form which form p/q 0.222...

Answer 1

Given:

0.22222222........

To find:

The p/q form of 0.222.......

Solution:

x = 0.222........ - eq.1

Multiplying both sides with 10 we get,

10x = 2.222....... - eq.2

Subtracting eq.1 from eq.2

10x = 2.222...........

- x = 0.222..........

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9x = 2.000...........

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9x = 2

Therefore, x = 2/9 which is in p/q form (p = 2 and q = 9) where q not equal to 0.

Information:

The above done method is called as x method of finding an non - Terminating recurring number to p/q form.

We must multiply both the sides with periodicity i.e on how much digits the bar is that many zeros after 1 must be multiplied.

Ex: 0.2 bar - since bar is on one digit we must multiply it with 10.

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