What do you call a fraction that cannot be written as a finite decimal?

For example, the fraction ⅓ cannot be written, because it repeats infinitely (0.33333333... etc). Is there a particular word for numbers that cannot be written directly, but must be expressed as fractions?

Solution 1:

Also Periodic decimal:

Richard Suchenwirth 2002-04-27 - Periodic decimal fractions are numbers where a sequence of digits behind the decimal point (the period) is endlessly repeated,

for example:

1/7 = 0.142857142857.. 1/3 = 0.3333..

Repeating decimal appears to be the most common definition according to : Ngram

Source:http://wiki.tcl.tk/3310

Solution 2:

Do you mean a recurring decimal?

A decimal number that has digits that repeat forever.

[Math is Fun]

Solution 3:

Is there a word for numbers that can be expressed as fractions but not as finite decimals? Not exactly.

There is a word for numbers that cannot be expressed as fractions; they are called irrational numbers.

Any number that can be expressed as a fraction is a rational number. However, this term encompasses both numbers like 1/3 that have repeating decimal representations, and numbers like 1/2 that don't.

Any number that, like 1/3, has a decimal number that repeats endlessly, is called a repeating decimal or recurring decimal.

There are also numbers like pi and e that have decimal portions that neither terminate nor repeat. I believe, however, that these numbers are always irrational, meaning they cannot be represented as fractions.

If that is the case--and I welcome corrections from any mathematicians slumming on the ELL board--then all of the numbers you refer to would be repeating/recurring decimal numbers.