Question

what is the value of 2.23 bar​

Answer 1

Answer:

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Answer 2

$\displaystyle \bf{ 2. \overline{23} = \frac{221}{99} }$

Given :

$\displaystyle \sf{ The \: number \: \: 2. \overline{23} }$

To find :

The value of the number

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 2. \overline{23} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 2. \overline{23} }$

Then x = 2.232323... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 223.232323... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 221

$\displaystyle \sf{ \implies x = \frac{221}{99} }$

$\displaystyle \sf{ \therefore \: \: 2. \overline{23} = \frac{221}{99}}$

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

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