Question

please give me answer ​

Answer 1

Question: Express 0.999... in the form of p/q

Solution:

Let x = 0.999..... --------(1)

As only one digit is repeating, we will multiply it with 10 on both sides.

Multiplying eq(1) by 10

10× x = 10 × (9.999....)

10x = 9.999... ----------(2)

Subtracting eq (2) from eq(1)

i.e. eq(2) - eq(1)

10x - x = 9.999... - 0.999...

9x = 9

x = 9/9

x = 1

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Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

Express 0.999........ in the form of p/q

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

Let,

• $\sf{\:y\:=\:0.\={9}......(1)}$

As there one number under bar ,

So, multiply by 10 on the both side,

$\mapsto\sf{\:10y\:=\:0.\={9}\times 10} \\ \\ \mapsto\sf{\:10y\:=\:9.\={9}.....(2)}$

Subtract equation (2) - equation (1)

$\mapsto\sf{\:9y\:=\:(9.\={9}\:-\:0.\={9})} \\ \\ \mapsto\sf{\:9y\:=\:9} \\ \\ \mapsto\sf{\:y\:=\:\dfrac{9}{9}} \\ \\ \mapsto\sf{\:y\:=\:1\:\:\:\:Ans}$

$\Large{\underline{\mathfrak{\bf{\pink{Hence}}}}}$

$\bigstar\sf{\:0.\={9}\:in\:form\:of\:\dfrac{p}{q}\:will\:be\:=\:1}$

Additional Knowledge

If any number have bar .

So, that's means this number will be going on infinite (∞) times .