Question

Is 0.363636... a repeating decimal?

Answer 1

Yes, `0.363636...` is a repeating decimal. It can be written as `0.bar36`.

`0.333333...` is also a repeating decimal; it can be written as `0.bar3`.

Answer 2

In a decimal. none, some or all of the digits can recur.
`0363636..` has two recurring digits.

Explanation:

`0.375` is a terminating decimal. None of the digits recur.
The fraction is `3/8`

`0.3333... = 0.bar3` is a recurring decimal.
The fraction is `1/3`

`0.947777 = 0.94bar7` Is a recurring decimal. The fraction is `853/900`

`4.382382... = 4.bar382` is a recurring decimal. The fraction is `4 382/999`

All of these decimals are rational numbers, they can all be written as fractions.

Some decimals continue to infinity without recurring. They cannot be written as fractions and are irrational numbers.

`pi = 3.1415926535............??????????`

In this case `0.363636....` is a recurring decimal.
It can be written as `0.dot3dot6 or 0.bar(36)`

A useful short cut to find the fraction is:

If all the digits recur, write a fraction as:

`"the recurring digits"/" a 9 for each digit"`

`0.363636 ... = 36/99 = 4/11`

Answer 3

`0.bar(36)=4/11`

Explanation:

One further note on this question - we can find the fraction that is associated with `0.bar(36)`:

If we set `x=0.bar(36)`, then `100x=36.bar(36)`, and so:

`100x-x=99x=36=36.bar(36)-0.bar(36)`

and so `99x=36 => x=36/99=4/11`