Math, asked by urja6078, 9 months ago

0.001 ( bar on 001) when expressed in the form if p/q is

Answers

Answered by MisterIncredible
8

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Question :

0.001 ( bar on 001) express this in p/q form ?

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Answer :

Given :

0.001 ( bar on 001)

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Required to find :

  • p/q form of 0.001 ---- (bar on 001)

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Solution :

0.001 (bar on 001)

\tt{\small{Let,\:x = 0.001001001001------ }{\red{\longrightarrow{Equation\;-\;1}}}}

Period = 001

Periodicity = 3

Since, the Periodicity is 3 .

Multipy the equation 1 with 1000

So,

Multiply with 1000 on both sides ;

\tt{\small{1000(x) = 1000(0.001001001001----)}}

\tt{\small{ 1000x = 001.001001001---}{\red{\longrightarrow{equation \;-\;2}}}}

Now,

Subtract equation - 1 from equation - 2

Hence ,

We get,

\tt{\large{1000x = 001.001001001 ----}}

\tt{\large{ \;\;\;\:  \:  \:  \:  \:  \:  \:x = \:  \:  \:  \:  \:  \:0.001001001 ----}}

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\tt{\large{999x = 001. 00000000-----}}

\large{\implies{\tt{ x = \dfrac{1}{999}}}}

Therefore,

\huge{\tt{0.}}{\overline{001}{\tt{= \dfrac{1}{999}}}}}

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Additional Information :-

What is period ?

Period is the numbers which are repeating .

For example :

Find the period of 5.333---

Here, period = 3

Similarly,

What is periodicity ?

Periodicity is the number of digits which are repeating in that sequence .

For example :

Find the Periodicity of 1.232323----

Here, periodicity = 2

Only a non - terminating repeating / recurring decimal can only be converted into the p/q form .

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Answered by Anonymous
1

  \mathtt{  \huge{\fbox{Solution :)}}}

Let ,

x = 0.001001 .... --- eq (i)

Multiply eq (i) by 1000 , we get

1000x = 1.001001 .... --- eq (ii)

Now , subtract eq (i) from eq (ii) , we get

 \sf \mapsto 1000x - x = 1.001001 \:  .... - 0.001001  \: .... \\  \\  \sf \mapsto</p><p>999x = 1 \\  \\  \sf \mapsto</p><p>x =  \frac{1}{999}

Hence , 0.001001 .... = 1/999

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