0.324 with a dot only above the 4
373.3333
Repeating Decimal
In the decimal expansion of , the digit repeats indefinitely.
A terminating decimal reaches an end after a finite number of digits whereas a repeating decimal, after a finite number of digits, has a string of decimals (also of finite length) that repeats forever. Thus 1.2356 is a terminating decimal. 1.456333... is a repeating decimal with the digit 3 repeating an infinite number of times. So also is 23.56142857142857...... where the string 142857 repeats to infinity. In fact, terminating decimals may be viewed as repeating decimals with zero repeating infinitely.
I think you mean 0.1333…, where the '3' repeats infinitely. This is equal to 4/30 = 2/15. However, if you mean 0.1333, literally - where the decimal terminates after the third '3', then, this is equal to 1,333/1,0000 .
It is a recurring decimal
76.666 (the decimal repeats infinitely).
373.3333
That's a repeating decimal. Some people call it a recurring decimal.
18/35 = 0.5142857142857... (142857 repeats infinitely)
A repeating decimal is a decimal that contains a series of numbers that repeat indefinitely. Examples include: 3.44444... 4.565656... 2.356356356... An ellipsis (...) at the end of the decimal signals that it repeats indefinitely.
They form a proper subset of rational numbers.
Repeating Decimal
A terminating decimal number is one whose decimal representation ends after a final number of digits. A non-terminating decimal number is one whose decimal representation goes on forever. It could be in the form of a number-string that repeats infinitely, for example, 2/11 = 0.18181818.... or one in which there is no pattern (all irrational numbers). Analogous definitions apply to numbers expressed in other bases.
a decimal that repeats is called a repeating decimal
23/3 is about 7.67. (The nature of the fraction means its decimal repeats infinitely, so it'd actually be 7.6666666…)
Not necessarily. If the decimal terminates, or if it repeats periodically, then it is rational.