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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.
What fractions could become a repeating decimal?
Any fraction with a denominator which has a prime factorization that includes any prime other than 2 or 5, it can produce repeating decimals.If the prime factorization of the denominator does not include 2 nor 5 then the decimal representation will be a repeating decimal.
How can you tell if a rational number is repeating without dividing?
If the denominator has ANY prime factor other than 2 or 5, then the decimal is repeating.
What is the answer if it is repeating decimal?
It is a rational number which, in its simplest form, has a denominator with a prime factor other than 2 and 5.
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 terminating decimals and repeating decimal reflected in fractions?
If a fraction, in its simplest form has a denominator whose only prime factors are 2 or 5, then the fraction is terminating. If the denominator has any other prime factor then the decimal is repeating.
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.
What examples represents a repeating decimal?
Any rational fraction such that, in its simplest form, the denominator contains a prime factor other than 2 and 5 will be a repeating decimal.
How to create repeating decimals?
If the ratio, in its simplest form, has a denominator which has any prime factor other than 2 or 5, you will have a repeating decimal.
How does 1 over 3 to 100th power have a repeating or terminating decimal representation?
It is repeating. Any fraction in simplest terms which has ANY prime factor other than 2 or 5 in its denominator will be a repeating fraction.
How can you predict whether a quotient will be terminating decimal or a repeating decimal?
If the denominator of the fraction, when written in its simplest form, has any prime factor other than 2 or 5 then it will be a repeating decimal fraction otherwise it will terminate.
What can you predict whether a quotient will be a terminating decimal or repeating decimal?
If the denominator of the fraction, when written in its simplest form, has any prime factor other than 2 or 5 then it will be a repeating decimal fraction otherwise it will terminate.
You are given a fraction in simplest form the numerator is not zero when you write the fraction as a decimal it is a repeating decimal which numbers from 1 to 10 could be the denominator?
You can get a repeating fraction with any denominator whose prime factors include some numbers other than 2 or 5. This is because 2 and 5 are the prime factors of 10 - the base of our decimal system. In this case, the denominator can be any of: 3, 6, 7, 9
