Question

Express 2.317 bar in p upon Q form where p and q are integers and q is not equals to zero​

Answer 1

Answer:

let 2.317 bar = 2.317317 bar = x..............(1)

multiply both sides by 1000,we get

2317.317bar = 1000 x...............(2)

subtracting 2 from 1, we get

999x = 2315

so, x = 2315/999

so, p= 2315

q = 999

Answer 2

Answer:

The $\frac{p}{q}$ form of $2.\overline{317}$ is $\frac{2315}{999}$ where  $p$, $q$ are integers and $q\neq 0$.

Step-by-step explanation:

Step 1 of 4

Consider the given number as follows:

$2. \overline {317}}$

or,

$2. \overline {317}}=2.317317317...$

Now, let $x=2. \overline {317}}$. Then,

$x=2.317317...$ . . . . . (1)

Step 2 of 4

Observe that the three digits $317$ are repeating.

So, multiply both the sides of equation (1) by $1000$.

⇒ $1000x=1000\times2.317317...$

⇒ $1000x=2317.317...$ . . . . . (2)

As $2317.317317...$ can be written as sum of two numbers, i.e.,

$2317.317317... =2315+2.317317...$

⇒ $2317.317317... =2315+x$ (Since $x=2.317317...$)

Substitute the value $2315+x$ for $2317.317317...$ in the equation (2) as follows:

⇒ $1000x=2315+x$

Step 3 of 4

Compute the value of $x$.

⇒ $1000x-x=2315$

⇒ $999x=2315$

⇒ $x=\frac{2315}{99}$ . . . . . (3)

Step 4 of 4

Expressing $2.\overline{317}$ in the $\frac{p}{q}$ form:

On comparing (1) and (3), we get

$2.317317=\frac{2315}{999}$

⇒ $2.\overline{317}=\frac{2315}{999}$

Here, $p=2315$ and $q=999$ are integers where $q\neq 0$.

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