Question

Express 0.5444444.......... recurring decimsls as fraction in their lowest term

Answer 1

let the irrational number be represented as x.
=> x= 0.5444444....
=> 10x = 5.444444... (multiplying 10 to both sides)
=> 10x - x = 5.4444444..... - 0.54444444
clearly all the 4s will get cancelled.
=> 9x = 4.9
=> x = 49/90
earlier we took x = 0.544444...
and at the end of our calculation, x = 49/90
=> 0.5444444..... = 49/90 {in the lowest term too}

Answer 2

$0.5444444..... = 0.5 \bar{4}$

$Let \: x = 0.5\bar{4} \\ \\ Multiply\: \: by \: \:10\: \: on\: \: both \:\: sides, \\ \\ 10x = 5.\bar{4} \\ \\ As \: \: there \: \: is \: \: one \: \: number \:\: under \:\: bar, multiply \: \: by \:\: on \:\: both,$

$100x = 54. \bar{4} \\ \\ \\ sutrac t \: 10x \: from \: both \: sides \\ \\ \\ 100 x = 54. \bar{4} \\ \: 10x = 5. \bar{4}\\ - - - - \\ 90x = 49 \\ - - - - \\ \\ x = \frac{49}{90}$


Hence,

$0.5 \bar{4} = \frac{49}{90}$