Question

Express 2.234(bar on 34)in the form of
p upon q
,where p and q are integers and q ≠ 0.​

Answer 1

Answer:

2.2343434... = 1106/495

( For proof , refer to the attachment ^_^" )

Solution:

Let the given number be x .

Thus,

x = 2.2343434.... ---------(1)

Multiplying eq-(1) both the sides by 10 ,

We get ;

=> 10x = 10 × 2.2343434....

=> 10x = 22.343434.... -----------(2)

Now,

Multiplying eq-(2) both the sides by 100 ,

We get ;

=> 100 × 10x = 100 × 22.343434....

=> 1000x = 2234.343434.... -------(3)

Now,

Subtracting eq-(2) from eq-(3) , we get ;

=> 1000x - 10x = 2234.343434...

–22.343434...

=> 990x = 2212

=> x = 2212/990

=> x = 1106/495

=> 2.2343434... = 1106/495

Hence,

Required answer is 1106/495