Question

Express 4.125 bar in the form of p/q

Answer 1

Hello dear

x = 4.125125125.......................[ 1 ]

1000x = 4125.125125..............[ 2 ]

[ 2 ] - [ 1 ]

1000x - x = (4125.125......) - (4.125......)

=> 999x = 4121

=> x = 4121/999

Hope it helps.

Answer 2

$let \: x = 4.125 \: bar \: \: \: ....(1)\\ multiply \: 1000 \: on \: both \: the \: sides \: in \: equation \: (1) \\ 1000x = 4125.125 \: \: \: ....(2) \\ subtract \: (1) \: and \: (2) \\ 999x = 4121 \\ x = \frac{4121}{999}$
Now 4.125 is in the form of
$\frac{p}{q}$
$= \frac{4121}{999}$