Question

Express 0.124in p/q form where 124 are bar

Answer 1

$\displaystyle \bf{ 0. \overline{124} = \frac{124}{999} }$

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

Given :

The number $\displaystyle \sf{ 0. \overline{124} }$

To find :

To express in the form p/q where p , q are integers and q ≠ 0

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. \overline{124} }$

Step 2 of 2 :

Express in the form p/q where p , q are integers and q ≠ 0

$\displaystyle \sf{ Let \: \: x = 0. \overline{124} }$

Then x = 0.124124124... - - - - - - - (1)

Multiplying both sides by 1000 we get

1000x = 124.124124124... - - - - - - (2)

Equation 2 - Equation 1 gives

999x = 124

$\displaystyle \sf{ \implies x = \frac{124}{99} }$

$\displaystyle \sf{ \therefore \: \: 0. \overline{124} = \frac{124}{999}}$

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

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Answer 2

123/990

Step-by-step explanation:

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