Question

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Answer 1

Answer:

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Answer 2

Question :-

To express $\sf0.\overline{001}$ in the form p/q in it's simplest form.

Answer :-

$\sf Let\: x = 0.\overline{001}$

Multiplying x by 1000x,

$\implies \sf1000 \times 0.\overline{001}$

$\implies \sf 001.\overline{001}$

• Subtracting the initial value from the value we obtained by multiplying it with 1000,

$\implies \sf 1000x - x = 001.\overline{001} - 0.\overline{001}$

• $\overline{001}$ gets cancelled in both the terms.
• Subtracting 1000x - x,

$\implies \sf 999x = 1$

Transposing 999,

$\implies \sf x = \dfrac{1}{999}$

Therefore,

$\sf 0.\overline{001}$ in the simplest fraction form is $\sf \dfrac{1}{999}$

Rational numbers :-

Rational numbers are those which can be expressed in the form p/q where p and q are co - primes and q ≠ 0.

Natural numbers, Whole numbers, Fractions, Integers and decimals all come under the category of rational numbers.

Decimal representation of rational numbers :-

Decimal numbers which come under Rational numbers are of 2 types.

• Terminating decimals
• Non terminating repeating/recurring decimals.

Terminating decimals :-

Decimals which come to a stop after a few numbers. They have a finite number of digits only.

Example :- 0.123, 456.8769 etc.

Non terminating repeating/recurring decimals :-

Those decimals which are never ending. The digits are although repetitive. There are infinite number of rational numbers.

Example :-  $\sf 1.\overline{23}$, $\sf 89.\overline{45}$ etc.