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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.

Q: 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?

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0.875 is a terminating decimal and as a fraction it is 7/8

An irrational number is not a terminating decimal and it also can't be expressed as a fraction.

The decimal form of a fraction is either a terminating or recurring decimal.

Because it can be expressed as a fraction

To sum this answer up you half to turn the fraction into a decimal and if it ends that is terminating but if it keeps going it is called a repeating decimal EXAMPLES Terminating- 5/10=.5 Repeating- 1/3=.3333 (bar notation over the 3)

Related questions

When the fraction is in its simplest or reduced form, if the denominator has any factor other than 1, 2 or 5, it will not be possible to express the fraction as a terminating decimal.

0.875 is a terminating decimal and as a fraction it is 7/8

Because a terminating decimal is a rational number that can also be expressed as a fraction

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.

An irrational number is not a terminating decimal and it also can't be expressed as a fraction.

It is a terminating decimal and as a fraction it is 47/50 in its lowest terms.

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.

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.

A negative fraction need not be a terminating decimal. For example, -2/3 = -0.66... (repeating).

It is a terminating decimal and so it is a decimal representation of a fraction.

If that's a terminating decimal, 6464/10000 = 404/625 If that's a repeating decimal, it equals 64/99

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.