Respuesta :

A rational number can be written in the form:

[tex]\frac{p}{q}; \ called \ the \ ratio \\ \\ where \ p \ and \ q \ are \ whole \ numbers[/tex]

The number [tex]$q$[/tex] isn't equal to zero because the division by zero is not defined. So we can represent rational numbers by a repeating or terminating decimal, for instance in the following four exercises we have:

[tex]\frac{2}{3}=0.6666...=0.\stackrel{\frown}{6} \\ \\ \frac{5}{8}=0.625000...=0.625\stackrel{\frown}{0} \\ \\ \frac{3}{1}=3.000...=3.\stackrel{\frown}{0} \\ \\ \frac{3446}{2475}=1.392323...=1.39\stackrel{\frown}{23}[/tex]

we know that

A rational number is the quotient of two integers with a denominator that is not zero , and can be represented by a repeating or terminating decimal.

Repeating Decimal is a decimal number that has digits that go on forever

Terminating decimal is a decimal number that has digits that do not go on forever.

examples

[tex] \frac{1}{3} = 0.333... [/tex] (the [tex] 3 [/tex] repeats forever)----> Is a Repeating Decimal

[tex] 0.25 [/tex] (it has two decimal digits)----> Is a Terminating Decimal

therefore

the answer is

A rational number can be written as the ratio of one [tex] integer [/tex] to another and can be represented by a repeating or [tex] terminating [/tex] decimal

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