Question

Find out p/q form of 0.10 bar

Answer 1

X=4/11

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Answer 2

The p/q form of $\overline{0.10}$ is 10/99.

Given:

A non-terminating number $\overline{0.10}$.

To Find:

p/q form of $\overline{0.10}$.

Solution:

We need to find the rational form or p/q form of  $\overline{0.10}$, where q is

non-zero.

To convert the given non-terminating number into a rational number or p/q form, we will use the following steps.

Step 1: Let us assume that the given number is x.

⇒ x = $\overline{0.10}$ = 0.101010....           ..........................(I)

Step 2: On multiplying this number by 100, we obtain:

100x = 10.101010...                   ..........................(II)

Step 3: Subtracting (I) from (II), we get;

100x - x = 10.101010... - 0.101010....

⇒ 99x = 10

⇒ x = 10/99.

We have obtained the rational form or p/q form of  $\overline{0.10}$ and it is 10/99.

∴ The p/q form of $\overline{0.10}$ is 10/99.

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