Question

explain each of the following in p upon Q form 2.31 7317 317​

Answer 1

Answer:

let x = 2.317 bar

so,1000x=2317.317bar

999x=1000x-x =2315

so, x =2315/999

2315/999is in the form of p/q

this is ur answer hope it help u

Answer 2

Answer:

The p upon q form of the number $2.317317317...$ is $\frac{2315}{999}$.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$2.317317317...$

or,

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

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

$x=2.317317317...$ ____ (1)

Step 2 of 3

Notice that the three-digits 317 are repeating.

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

⇒ $1000x=1000\times2.317317...$

⇒ $1000x=2317.317317...$ ____ (2)

Rewrite the number $2317.317317....$ as follows:

⇒ $2317.317317...=2315 + 2.317317...$

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

Substitute the value of $2317.317317...$ in the equation (2) as follows:

⇒ $1000x=2315+x$

Step 3 of 3

Find the value of $x$.

⇒ $1000x-x=2315$

⇒ $999x=2315$

⇒ $x=\frac{2315}{999}$

Final answer: The number $2.317317317...$ in the $p/q$ form, where $p$ and $q$ are integers and $q\neq 0$ is $\frac{2315}{999}$.

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