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A rational number is a number which can be represented as the ratio of two integers, p/q.
Consider dividing p by q. Either the remainder becomes zero at some stage so that the decimal representation is terminating. Otherwise, there is a remainder. With the divisor q, the only possible remainders are integers between 1 and q-1. There are thus only q-1 possible different remainders after which the remainder is one that has appeared before. When that happens the pattern from the previous occurrence of that remainder will repeat.
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Is every rational number a repeating decimal?
No. A rational number is any terminating numeral. A repeating decimal is irrational.
Is 0.454545... an irrational number?
No. It is a rational number. Any repeating decimal or terminating decimal is rational.
Is 5.7 repeating rational?
Yes. Any terminating or non-terminating recurring decimal is a rational number.
What is a decimal number that ends or recurs?
Decimal numbers that end or recur are known as terminating or repeating decimals. 0.75 is a terminating decimal. 0.4444 repeating is a repeating decimal.
Is 4.3333333 a rational number?
Yes- every terminating or repeating decimal number is rational.
