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Why can a decimal greater than 1 be a repeating decimal?
Any rational number, whose denominator has a prime factor other than 2 or 5 will have a decimal representation which is repeating. The size of the number, in relation to 1, is irrelevant.
How are fractions are related to repeating decimals and terminating decimals?
If the denominator of the fraction has any prime factor other than 2 or 5, then it has a decimal representation with a repeating sequence of digits. If the denominator is a product of any number of 2s or 5s then it can be represented as a terminating decimal.
Why do I get a repeating decimal when I divide?
When you get a repeating decimal when dividing, it means that the decimal representation of the quotient has a repeating pattern of digits. This occurs when the divisor (the number you're dividing by) is not a factor of 10, leading to a situation where the division process does not result in a clean, terminating decimal. The repeating decimal is a way to represent the fraction that results from the division in a concise form.
How fractions are related to repeating decimals and terminating decimals?
All rational fractions - one integer divided by a non-zero integer - give rise to repeating or terminating decimals. If, for the fraction in its simplest form, the denominator can be expressed as a product of powers of only 2 and 5 then the decimal will terminate. If the denominator has any prime factor other than 2 or 5 the decimal will be recurring. All non-rational fractions will have infinite, non-recurring decimal representations.
How do you know whether a number is non-terminating repeating?
A non-terminating repeating number must be rational. When its fractional part is in its simplest form, the denominator must have a prime factor other than 2 or 5.
