Question

express 0.66666...... in the form of p/q where p and q are integers and q \neq 0

Answer 1

$\displaystyle \bf{0.66666... = \frac{2}{3} }$

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

Given :

The number 0.66666...

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 0.66666...

Step 2 of 2 :

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

Let x = 0.66666... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 6.66666... - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 6

$\displaystyle \sf{ \implies x = \frac{6}{9} }$

$\displaystyle \sf{ \implies x = \frac{2}{3} }$

$\displaystyle \sf{ \therefore \: \: 0.66666... = \frac{2}{3} }$

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

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