Question

find the value of 0.423

Answer 1

$\displaystyle \bf{ 0. 4\overline{23} = \frac{419}{990} }$

Correct question : Find the value of $\displaystyle \sf{ 0. 4\overline{23} }$

Given :

The number $\displaystyle \sf{ 0. 4\overline{23} }$

To find :

The value of $\displaystyle \sf{ 0. 4\overline{23} }$

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. 4\overline{23} }$

Step 2 of 2 :

Find the value

$\displaystyle \sf{ Let \: \: x = 0. 4\overline{23} }$

Then x = 0.423232323... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 4.23232323... - - - - - - (2)

Again Multiplying both sides by 100 we get

1000x = 423.23232323... - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 419

$\displaystyle \sf{ \implies x = \frac{419}{990} }$

$\displaystyle \sf{ \therefore \: \: 0. 4\overline{23} = \frac{419}{990}}$

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