Question

Express 1.21212121.... as a fraction

Answer 1

that would be 1 21/99  or  120/99 as an improper fraction.

Answer 2

To solve such questions we will have to observe the fact that this is a repeating decimal number with the repeating figures being 2 and 1 as 21.

Thus, we can represent 1.21212121... as
`1.\overline{21}`

Let us represent the original number 1.21212121... by the letter "a". Thus,

a=1.21212121...=
`1.\overline{21}`

Therefore,
`a=1.\overline{21}`..................(equation 1)

Let us now multiply (equation 1) by 100 to get:

`100a=100* 1.212121...=121.\overline{21}`.....(equation 2)

Now, when we subtract (equation 2) from (equation 1), we will get:

`100a-a=121.\overline{21}-1.\overline{21}`

`99a=120`

`\therefore a=(120)/(99)`

Thus the given number 1.21212121... can be represented as a fraction as
`(120)/(9)`.