Is .6 a rational number?

A rational number is a number, which can be described as a ratio of two integers. As it is a ratio of integers, it can be positive as well as negative.

Further, any decimal fraction, which limits itself beyond the decimal point (such as `5.7` which does not go beyond tenth place) or has continuously repeats numbers (till infinity) beyond a certain place of decimal (such as `4.33333....` or `0.232142857142857142857....`) can be easily written as ratio of integers, however large and hence are rational.

Now as `0.6=6/10`, is a ratio of two integers, it is a rational number.

The basic rule: does it satisfy one of 2 conditions.

`color(blue)("Condition 1")` Is it a terminating decimal?

Example: 0.125 This stops after the 5 so it terminates

`color(white)(.)`

`color(blue)("Condition 2")` Is it a repeating decimal

Example: 0.356356356356....

written as `0.356bar356`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(olive)("If the decimal satisfies either of these 2 conditions then, yes.")`
`color(olive)("A rational number is a number that can be written in the form of a fraction")`

`color(magenta)("By the way the counting numbers are rational")`

`color(magenta)(1/1"; "2/1"; "3/1"; "4/1...."& so on")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(red)("Answering your question")`

`0.6 =6/10` as this can be written as a fraction it is a rational number.