Question

Find the value of 56.08[148] /14. (The number 148 in the bracket is non terminating recurring)​

Answer 1

Answer:

$\frac{56.08148148.....}{14}=\frac{\frac{7571}{1890}$

Step-by-step explanation:

First we write

56.08148148148................... in $\frac{p}{q}$ form

Let

$x = 56.08148148..............................$............(1)

Multiply (1) by 100 we get

$100x=5608.148148.....................$..........(2)

Multiply (2) by 1000, we get

$100000x=5608148.148148.....................$..........(3)

(3)-(2) gives

$100000x-100x=5602540$

$99900x=5602540$

$9990x=560254$

$x=\frac{560254}{9990}$

$x=\frac{280127}{4995}$ ( reduced by 2)

$x=\frac{7571}{135}$ ( reduced by 13)

Now,

$\frac{56.08148148.....}{14}$

$=\frac{\frac{7571}{135}}{14}$

$=\frac{\frac{7571}{135*14}$

$=\frac{\frac{7571}{1890}$