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?
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,
1/7 = 0.142857142857.. 1/3 = 0.3333..
Repeating decimal appears to be the most common definition according to : Ngram
Do you mean a recurring decimal?
A decimal number that has digits that repeat forever.
"Periodic decimal" is actually a name for a representation of such numbers, just as vulgar fraction is a name for the representation
One could call the numbers themselves:
- Numbers which have a periodic decimal representation.
- Rationals which in their simplest form
qhas a factor other than 2 or 5.
This is another way of saying that the numbers themselves do not really have a name used by mathematicians. The reason for this is that the decimal representation is not usually considered particularly special.
One can for example represent ⅓ in ternary exactly as
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.