Question

Express the value of 0.423 in p/q form where bar is on 23.

Answer 1

Answer:

The $\frac{p}{q}$ form of 0.42323....... = $\frac{419}{990}$

Step-by-step explanation:

Let us take x = 0.4232323....... -----------------(1)

Here, in the decimal part, one term is not recurring,

Hence multiplying equation (1) by 10 on both sides we get

10x = 4.232323.......----------------------.(2)

Since there are two recurring decimals, multiply the equation (2) by 100 on both sides

10x ×100 = 4.232323.......×100

1000x = 423.2323.............. -------------------------(3)

To eliminate the decimal part, subtract equation (2) from equation (3) we get

1000x - 10x = 423.2323.......- 4.2323.......

990x = 419

x = $\frac{419}{990}$

0.42323....... = $\frac{419}{990}$

The $\frac{p}{q}$ form of 0.42323....... = $\frac{419}{990}$

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Answer 2

Answer:

The value of $0.4\overline{23}$ in the p/q form is $\frac{419}{999}$.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$0.4\overline{23}$

or,

$0.4\overline{23}=0.4232323...$

Now, let $x=0.4\overline{23}$. Then,

$x=0.4232323...$ ____ (1)

Step 2 of 3

Notice that after the decimal only two-digits are repeating. So,

Multiply both the sides of the equation $(1)$ by $10$.

⇒ $10x=10\times0.4232323...$

⇒ $10x=4.232323...$ ____ (2)

Also,

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

⇒ $1000x=1000\times0.4232323...$

⇒ $1000x=423.232323...$ ____ (3)

Step 3 of 3

Find the value of $x$.

Subtract the equation (2) from the equation (3) as follows:

⇒ $1000x-10x=423.232323...-4.232323...$

⇒ $990x=419$

⇒ $x=\frac{419}{999}$

Therefore, the value of $0.4\overline{23}$ in the p/q form is $\frac{419}{999}$.

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