Yes, there is a pattern to terminating fractions. A fraction will terminate if its denominator, when fully simplified, has no prime factors other than 2 and 5. This is because the decimal representation of such fractions can be expressed in a base that matches the prime factors of 10 (the base of our decimal system). For example, fractions like 1/2, 3/5, and 7/20 terminate, while fractions like 1/3 or 2/7 do not.
All rational fractions.
Yes.
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Terminating fractions create a digital equivalent of fixed length (e.g. 1/4 = exactly 0.25). Non-terminating (repeating) fractions create a repeating decimal after a certain number of places, and do not have an exact digital equivalent (e.g. 1/3 = 1.333_). (This occurs as a result of conversion to base-10 numbers.)
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All terminating decimals can be written as fractions.
All rational fractions.
Yes.
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Terminating fractions create a digital equivalent of fixed length (e.g. 1/4 = exactly 0.25). Non-terminating (repeating) fractions create a repeating decimal after a certain number of places, and do not have an exact digital equivalent (e.g. 1/3 = 1.333_). (This occurs as a result of conversion to base-10 numbers.)
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That they can be converted into fractions
If they are non-terminating and there is a repeating pattern, then they are rational. If they are non-terminating and there is no repeating pattern, as in pi, they are irrational.
A fraction will have a terminating decimal if the prime factorisation of the denominator contains only the primes 2 or 5, or both.
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.
Any terminating/rational number can be written as a fraction.
fractions or decimals