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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 is a rational number either terminating or repeating?
A rational number is expressed as the quotient of two integers, where the denominator is not zero. When expressed in decimal form, this fraction can either terminate (end after a certain number of digits) or repeat (enter a cycle of digits). This behavior arises from the division process; if the denominator has only the prime factors 2 and/or 5, the decimal will terminate. Otherwise, the division will eventually lead to a repeating cycle due to the finite number of possible remainders in the long division process.
Why do I get a repeating decimal when I divide?
Any TERMINATING decimal can be written as a fraction with a denominator that is a power of 10 - which has the prime factors 2 and 5. Therefore, any fraction (in simplest terms) must have a denominator which is only made up of the prime factors 2 and 5. Any other factor, and the fraction will not be terminating.As to why it repeats, that's because in the division, there are only so many options. For example, if you divide by 7, the remainder, in each step of the division, can only be a number between 1 and 6. Eventually, the pattern will repeat.
What kind of denominators make a decimal repeat?
A decimal repeats when the denominator of a fraction, in its simplest form, contains prime factors other than 2 and 5. This occurs because only fractions with denominators that are products of these prime factors can be expressed as terminating decimals. For example, the fraction 1/3 has a denominator of 3, which leads to the repeating decimal 0.333..., while 1/4 has a denominator of 4, resulting in the terminating decimal 0.25.
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
