Question

express 0.254 as a fraction in simplest form

bar on 54

Answer 1

$\displaystyle \bf{ 0. 2\overline{54} = \frac{14}{55} }$

Given :

The number $\displaystyle \sf{ 0. 2\overline{54} }$

To find :

To express as a fraction in simplest form

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. 2\overline{54} }$

Step 2 of 2 :

Express as a fraction in simplest form

$\displaystyle \sf{ Let \: \: x = 0. 2\overline{54} }$

Then x = 0.254545454... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 2.54545454... - - - - - - (2)

Multiplying both sides of Equation 2 by 100 we get

1000x = 254.54545454... - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 252

$\displaystyle \sf{ \implies x = \frac{252}{990} }$

$\displaystyle \sf{ \implies x = \frac{14}{5} }$

$\displaystyle \sf{ \therefore \: \: 0. 2\overline{54} = \frac{14}{55}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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Answer 2

Answer:

0.2545454.......... $= \frac{126}{495}$

Step-by-step explanation:

The given number is 0.254545454.............

Required to convert it into a fracton

Solution

Let, x = 0.2545454.......... -----------------(1)

Multiplying (1) with '10' on both sides

10x = 2.545454........ ------------------(2)

Multiplying equation(2) with 100

1000x = 254.5454........-----------(3)

Subtracting (2) from (3)

1000x - 10x = 252

990x = 252

x = $\frac{252}{900}$

$= \frac{126}{495}$

∴0.25454.....  $= \frac{126}{495}$

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