# Is 0.375 rational or irrational?

Apr 11, 2015

Anything that can be expressed as a fraction with an integer numerator and an integer denominator is rational.

$0.375 = \frac{375}{1000}$
and is therefore rational.

Any number which when written as a decimal form which terminates (that is ends with only $0$-value digits following the last digit) or any decimal form number that ends with a sequence which repeats indefinitely is rational.

For example, both
$0.3750000 \left[0. . .\right]$
and
$6.7292929 \left[29. . .\right]$ (with the $29$ pattern repeating forever)
are rational

An irrational number might look like:
$4.37337333733337 \ldots$ where the number of $3$'s between $7$'s increases by $1$ with each segment of the series
(Note this is only an example. There are many different ways in which the sequence can be non-repeating).