Is 0.375 rational or irrational?

1 Answer
Alan P.
Apr 11, 2015

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

#0.375 = (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[0...]#
and
#6.7292929[29...]# (with the #29# pattern repeating forever)
are rational

An irrational number might look like:
#4.37337333733337...# 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).

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