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If A over B is a fraction in simplest form with A and B counting numbers and a terminating decimal form why must B be a factor of a power of 10?
Wiki User
∙ 6y ago
Suppose A/B equals a decimal fraction F, which has d digits after the decimal place and then terminates.Then (A/B)*10D = F*10D is an integer.
That is A*10D/B is an integer.
A and B are coprime so they have no factor in common and therefore B must divide 10D.
Wiki User
∙ 6y ago
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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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It is a terminating decimal and so it is a decimal representation of a fraction.
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A negative fraction need not be a terminating decimal. For example, -2/3 = -0.66... (repeating).
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Reduce the fraction to its simplest form - that is, remove any common factors between the numerator and denominator. If the denominator now is a factor of some power of 10, that is, if the denominator is of the form 2a*5b then the fraction will me a terminating decimal. If not, it will not.
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If that's a terminating decimal, 6464/10000 = 404/625 If that's a repeating decimal, it equals 64/99
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