Question

Express 0.6666.....in p/q form

Answer 1

Answer:

Let x = 0.6 bar = 0.666666666……

Multiplying both side by 10 you will get

10x = 6.6666666…..

10x = 6 + 0.66666….

10x = 6 + x

9x = 6

x = 2/3

Hence the p/q form of 0.6 bar = 2/3 ans.

Answer 2

$\displaystyle \bf{0.6666... = \frac{2}{3} }$

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

Given :

The number 0.6666...

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 0.6666...

Step 2 of 2 :

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

Let x = 0.6666... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 6.6666... - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 6

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

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

$\displaystyle \sf{ \therefore \: \: 0.6666... = \frac{2}{3} }$

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

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