Question

convert the following into rational number in the form of p/q...class 9th maths...
plz solve this​

Answer 1

Question -

Convert the following into rational numbers in the form of p/q-

$14.\overline{141}$

Solution -

$Let, x = 14.141141.....1)$

Since three digits are repeating so we should multiply both sides by 1000

$1000x = 14141.141141.....2)$

Now,

2) - 1) we will get -

$1000x - x = 14141.141141.... - 14.141141...$

$999x = 14127$

$x = \frac{14127}{999}$

$x = \frac{4709}{333}$

$We \: can \: also \: check \: the \: reverse \: \\ \: that \: \frac{4709}{333} =14. \overline{141}$

So, every number with a non-terminating recurring decimal expression can be expressed in the form of p/q where p and q are integers and q not equal to 0.