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Numbers that can be expressed as fractions are called rational. A number that cannot be written as a fraction is called irrational. Common examples of this are the square root of 2, e, pi, etc*.

Real numbers (which include irrational and rational numbers) can be described by decimal expansions (possibly infinite ones). If a number has a decimal representation that repeats it must also be able to be represented as a fraction.

* (the last two of these are also transcendental, which essentially means they cannot be described as a solution to certain equations).

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Q: What is a number that cannot be written as a fraction a decimal that is non repeating non terminating?
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How do you determine whether you can write a given decimal as a fraction?

If the decimal is terminating or repeating then it can be written as a fraction. Decimal representations which are non-terminating and non-repeating cannot be expressed as a fraction.


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The latter which would be an irrational number that cannot be expressed as a fraction.


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Any rational number is either a repeating decimal, or a terminating decimal.


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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.


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As written, it's terminating.


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215 is a terminating decimal, as it does not repeat infinitely. It can be written as 215.000000... or 215.


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