Question

Express 0.254 bar on 54 as a fraction in simplest form


Class 10

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Answer 1

$\huge \bf{HEY \: FRIENDS!!}$

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$\huge \bf \underline{Here \: is \: your \: answer↓}$

⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

$\boxed{Convert \: into \: \: \frac{p}{q} \: form \: or \: fraction.}$

▶⏩ 0.254 bar on 54.

$\bf{ = > Let \: x = 0.25454.........(1).}$

$\boxed{Multiply \: both \: side \: by \: 10.}$

$\bf{=> 10 × x = 10 × 0.25454...}$

$\bf{=> 10x = 2.5454........(2).}$

$\boxed{Now, \: multiply \: both \: side \: by \: 100.}$

$\bf{=> 100 × 10x = 100 × 2.5454...}$

$\bf{=> 1000x = 254.5454.......(3).}$

$\boxed{Now, \: substract \: equation \: (3) \: and \: (2).}$

$\bf{=> 1000x - 10x = 254.5454 - 2.5454.}$

$\bf{=> 990x = 252.}$

$\bf = > x = \frac{252}{990} .$

$\huge \bf{ = > x = \frac{14}{55} .}$

✅✅ Hence, it is converted into p/q form or fraction ✔✔.

$\huge \boxed{THANKS}$

$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$

Answer 2

Let x = 0.254



• First reduce all extra numbers except bar numbers after decimal,

So, to make it, multiply by 10on both sides as there is only one extra number,



=> 10x = 10 × 0.254 bar
=> 10x = 2.54 bar



Then, As there are 2 numbers under bar, multiply by 100


=> 1000x = 254.54 bar



Subtract 10x from both sides,



1000x = 254.54 bar
_(-)10x =_(-)2.54_bar
990x = 252 [ bar cancel ]
______________


$x = \frac{252}{990} \\ \\ \\ x = \frac{3 \times 84}{3 \times 330} = \frac{28 \times 3}{110 \times 3} = \frac{28}{110} = \frac{14 \times 2}{55 \times 2} = \frac{14}{55}$





Hence, 0.254 ( bar ) in p/q form is equal to 14/55