Question

Express 0.131313……. in p/q form​

Answer 1

Steps to convert decimal to fractions.

x = 0.131313.... (1)

100x = 13.1313.....  (2)

(As the recurring part (13), is of two digits, we multiply by 100 so that decimal parts of x and 100x are the same)

Subtracting (1) from (2)

100x - x = 13.131313.....- 0.131313...

99x = 13

Hence,

$x = \frac{13}{99}$

So therefore,

0.13131313..... = $\frac{13}{99}$ in $\frac{p}{q}$ form

Answer 2

Answer:

$\frac{13}{99}$ is the required $\frac{p}{q}$ form.

Explanation:

A rational number is a particular class of real numbers in mathematics. Any integer that can be stated in the $\frac{p}{q}$form, with q ≠ 0, is referred to as it.

Given that, 0.131313...

Let x = 0.131313 ...........(i)

By multiplying both sides by 100 we get,

⇒ 100x = 13.1313........(ii)

Now, we subtract (i) and (ii) we get,

⇒ 100x - x = 0.1313131 - 13.1313131 = 13

⇒ 99x = 13

⇒ x = $\frac{13}{99}$

Final answer:

Hence, $\frac{13}{99}$ is the required $\frac{p}{q}$ form.

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