Question

Express 0.14bar in p/q form

Answer 1

Answer:

See this.

Step-by-step explanation:

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Answer 2

$\displaystyle \bf{ 0. \overline{14} = \frac{14}{99} }$

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

Given :

The number $\displaystyle \sf{ 0. \overline{14} }$

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 $\displaystyle \sf{ 0. \overline{14} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 0. \overline{14} }$

Then x = 0.14141414... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 14.14141414... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 14

$\displaystyle \sf{ \implies x = \frac{14}{99} }$

$\displaystyle \sf{ \therefore \: \: 0. \overline{14} = \frac{14}{99}}$

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

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