Question

Represent the rational number "0.2343434…" in the form of p/q , where p and q(q≠0) are integers.

Answer 1

Answer:

let x = 0.2343434...

10x=2.343434...

1000x =234.34343......

990x=232

x=232/990

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Answer 2

According to the above question

We have to find the given number as rational number .

The rational number form:

$\frac{p}{q} \: (q≠0)$

p and q are integers

Step-by-step explanation:

Given ,

$0.2343434…$

Step-1:

Let ,x= 0.2343434…

Multiply the above terms by 10 , we get and the value of Right hand side shift the decimal , we get

$10 \times x = 10 \times (0.2343434…)$

Multiply the terms

$10x = 2.343434… \: \: \: \: \: \: ...(1)$

Step-2:

Again multiply (1) by 10 , we get

$10 \times 10x = 10 \times 2.343434…$

$100x = 23.43434.... \: \: \: \: \: ....(2)$

Step-3:

Again multiply(2) by 10,we get

$10 \times 100x = 10 \times (23.43434....)$

$1000x = 234.3434... \: \: \: \: \: ...(3)$

Step-4:

Subtract the equation (3) and (1), we get

$1000x - 10x = 234.3434... - 2.3434...$

Simplify the terms

$990x = 234 - 2$

$990x = 232$

Shift 990 toward Right hand side as divison,

$x = \frac{232}{990} \: \: \: \: \: .......(4)$

Divide (4) by 2,

$x = \frac{232 \div 2}{990 \div 2}$

$x = \frac{116}{495}$

Hence ,

The rational form of "0.2343434…" is 116/495.

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