Question

Express the number in p/q form 0.512 bar on 512

Answer 1

Given:

The number is $0.\overline{512}$.

To find:

The p/q form of the given number.

Solution:

Let

$x=0.\overline{0.512}$

$x=0.512512...$         ...(i)

Multiply both sides by 1000.

$1000x=512.512512...$         ...(ii)

Subtracting (i) from (ii), we get

$1000x-x=512.512512...-0.512512...$

$999x=512$

Divide both sides by 999.

$x=\dfrac{512}{999}$

Therefore, the required number in the p/q form is $\dfrac{512}{999}$.

Answer 2

Answer:

Given:

The number is 0.\overline{512}0.512 .

To find:

The p/q form of the given number.

Solution:

Let

x=0.\overline{0.512}x=0.0.512

x=0.512512...x=0.512512...         ...(i)

Multiply both sides by 1000.

1000x=512.512512...1000x=512.512512...         ...(ii)

Subtracting (i) from (ii), we get

1000x-x=512.512512...-0.512512...1000x−x=512.512512...−0.512512...

999x=512999x=512

Divide both sides by 999.

x=\dfrac{512}{999}x=999512

Therefore, the required number in the p/q form is \dfrac{512}{999}999512 .

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