Question

Express 0.112 bar in the form of p/q, where p and q are integers and q is not equal to 0.

Answer 1

Answer:

Let n=0.112Bar-------------Equation 1.

Multiply by 1000:1000n=112.112------------------Equation 2.

Subtracting Equation 2 from equation 1,we get,999n=112.

Therefore,n=112/999.

Answer 2

Answer:

$0.\overline{112}$ in the p/q form, where p and q are integers and q≠0 is $\frac{112}{999}$.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$0.\overline{112}$

or,

$0.\overline{112}=0.112112...$

Now, let $x=0.\overline{112}$. Then,

$x=0.112112...$ . . . (1)

Step 2 of 3

Notice that the three-digits $112$ is on repeating.

Multiply both the sides of the equation (1) by $1000$.

⇒ $1000x=1000\times0.112112...$

⇒ $1000x=112.112112...$ . . . . . (2)

Rewrite the number $112.112112...$ as follows:

⇒ $112.112112...=112+0.112112...$

⇒ $112.112112...=112+x$

Substitute the value of $112.112112...$ in the equation (2) as follows:

⇒ $1000x=112+x$

Step3 of 3

Find the value of $x$.

⇒ $1000x-x=112$

⇒ $999x=112$

⇒ $x=\frac{112}{999}$

Therefore, $0.\overline{112}$ in the p/q form, where p and q are integers and q≠0 is $\frac{112}{999}$.

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