Question

express 0.1232323....in p/q form

Answer 1

Answer:

61/495

Step-by-step explanation:

x=0.1232323.....

10x=1.232323........ -1

1000x=123.232323........ -2

subrtact 2-1

990x=122

x=990/122=61/495

Answer 2

Given:

0.1232323...

To find:

The p/q form of 0.1232323...

Solution:

A number is called a rational number if it can be written in the form of p/q.

So,

we need to convert 0.1232323... or 0.12323 bar in rational form.

Let,

x = 0.1232323... (i)

On multiplying (i) by 10, we have,

10x = 10 × (0.1232323...)

10x = 1.232323... (ii)

Now,

On multiplying (i) by 1000, we have,

1000x = 1000 × (0.1232323...)

1000x = 123.2323... (iii)

Now, subtract (iii) from (ii),

1000x - 10x = 123.2323... - 1.232323...

990x = 122.000

(numbers after the decimal point are the same and hence, get subtracted out)

x = 122/990

x = 61/495

and x = 0.1232323... from (i)

So, the p/q form of 0.1232323... is 61/495.