Question

the value of 0.999......in the form of p/q where p and q are integers and q not equal to 0
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Answer 1

To Find :

• we need to find the value of 0.999.... in the form of p/q where p and q are intigers and q is not equal to 0.

Solution :

$\boldsymbol {0. \overline{9}}$

Let x = 0.999.....

Let x = 0.999...⠀⠀⠀⠀⠀⠀be equation (1).

As bar is on 1 Digit so, we should multiply Equation (1) by 10.

10x = 9.999....

Let 10x = 9.999 ....⠀⠀⠀⠀be equal (2)

Subtracting equation (1) from Equation (2)

• (2) - (1)

⠀⠀⠀⠀10x = 9.999.....

⠀⠀⠀⠀⠀ x = 0.999.....

⠀⠀⠀⠀ ⠀-- ⠀--⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀9x = 9

⠀⠀⠀⠀⠀⠀x = 9/9

⠀⠀⠀⠀⠀⠀x = 1

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Hence,

• 0.999... = 1

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