Question

Value of 2.1478 (bar on 478) in p/q form

Answer 1

$\huge{\underline{\bold{Solution:}}}$

The given expression is to be converted in the p/q form.

For this, let the first expression as x = 2.1478478......

Then, take two right side and put a decimal in it as 10x = 21.478478....

At last take 478 to right side and subtract the last two expression for the required answer.

Main solution is given below ;


$\bold{2 .1\bar4\bar7\bar8} \\ \\ \bold{let \: x = 2.1478478......(1)} \\ \\ \bold{10x = 21.478478........(2)} \\ \\ \bold{10000x = 21478.478478...(3)} \\ \\\bold{On \: subtracting \: (2) \: from \: (3)} \\ \\ \bold{10000x - 10x = 21478 - 21} \\ \\ \bold{9990x = 21457} \\ \\ \boxed{\bold{x = \frac{21457}{9990} }}$

$\bold{Hence\: it \: is \:in \: the \: p/q \: form.}$

$\huge{\underline{\bold{Thanks}}}$