Question

How to convert 2.43... in p/q form

Answer 1

Hi there

Hope this will help you

Thank You

Answer 2

In the given question : It's not mentioned whether there is any bar / vinculum / line / dot over the given decimals.

Case 1 : If there is no bar / vinculum / line / dot over the decimals.

= > 2.43

= > 2.43 / 1

Multiply the denominator and numerator by 100.

= > ( 2.43 x 100 ) / ( 1 x 100 )

= > 243 / 100

Hence required result is 243 / 100.

Case 2 : If there is bar / vinculum / line / dot over the decimals.

Let the required value of 2.43 vinculum ( or 2.$\bar{43}$ ) be a,

a = 2.$\bar{43}$ ... ( 1 )

As there is two number under bar, multiply by 10 on both sides,

= > 100 x a = 100 x 2.$\bar{43}$

= > 100a = 243.$\bar{43}$

Subtracting ( i ) from this equation :

100a = 243.$\bar{43}$

- a = - 2.$\bar{43}$

99a = 241 { bar cancel }

= > 99a = 241 [ bar cancel ]

= > a = 241 / 99

Hence the required numeric value of 0.23.. is 241 / 99.