Is 10.222... a rational number?

1 Answer
Sep 27, 2016

Yes, #10.22222......=92/9=10 2/9#

Explanation:

Yes, it is a rational number. In fact any decimal number which ends after a limited number of places beyond decimal point, or in which digits repeat endlessly after decimal place, are rational number.

Here in #10.222.............#, #2# gets repeated endlessly i.e. till infinity and hence is a rational number.

Let #x=10.22222....#, then #10x=102.2222.....#.

Subtracting first from second, we get

#9x=92#, hence #x=92/9# or

#10.22222......=92/9=10 2/9#