Express the following in the form displaystyle frac-p-q- where p and q are integers and qneq00-404040- -displaystyle frac-40-q- then what is the value of q -

Question

Express the following in the form displaystyle frac-p-q- where  p  and q are integers and qneq00-404040- -displaystyle frac-40-q- then what is the value of q -

Toppr Admin · Accepted Answer

Let x-0-404040-gt-100x-40-4040-gt-100x-40-0-4040-gt-100x-40-x-gt-100x-x2212-x-40-gt-99x-40-gt-x-4099Hence- q-99

Express the following in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$
$0.404040...$ = $\frac{40}{q}$ , then what is the value of $q$ ?

Let $x = 0.404040...$
$=> 100 x = 40.4040...$
$=> 100 x = 40 + 0.4040...$
$=> 100 x = 40 + x$
$=> 100 x - x = 40$
$=> 99 x = 40$
$=> x = \frac{40}{99}$
Hence, $q = 99$

Express the following in the form pq, where p and q are integers and q≠00.404040... =40q, then what is the value of q ?

Let x=0.404040...=>100x=40.4040...=>100x=40+0.4040...=>100x=40+x=>100x−x=40=>99x=40=>x=4099Hence, q=99

Express the following in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$
$0.404040...$ = $\frac{40}{q}$ , then what is the value of $q$ ?

Let $x = 0.404040...$
$=> 100 x = 40.4040...$
$=> 100 x = 40 + 0.4040...$
$=> 100 x = 40 + x$
$=> 100 x - x = 40$
$=> 99 x = 40$
$=> x = \frac{40}{99}$
Hence, $q = 99$