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Q: What fractions is represented by a terminating decimal?

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A fraction will have a terminating decimal if the prime factorisation of the denominator contains only the primes 2 or 5, or both.

There are infinitely many fractions which must be represented by non-terminating decimals, not just one.

All rational fractions.

Yes, it can be represented as a terminating decimal.

Yes, as represented in the question, it is.

0.5 is a terminating decimal and, since it is equal to a half, it is not an integer. A terminating decimal that is not an integer is a rational fraction. However, not all rational fractions are terminating decimals (eg 1/3 = 0.333...).0.1251.2512.5etc.

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.

No, not all fractions can be written as a non-terminating decimal. For instance, 1/3 has infinitely many 3's in the decimal places.

The rational fraction, one third, can be represented as a non terminating decimal, with the digit 3 repeating for ever.

No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.

That is the definition of a rational number.

No, a rational number, expressed as decimal, is either a terminating decimal, such as 1/4 = 0.25, or a repeating decimal, such as 1/7 = 0.142857 142857 142857 ...

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