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A rational number is a continuous quantity that is a quotient of two integers in which the second integer is a natural number. Rational numbers include the integers as well as non-integers such as fractions and decimals. Rational numbers are the direct result of the arithmetical operation of division.
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Is the quotient of an irrational number and a rational number always irrational?
No. It is not defined if the rational number happens to be 0.
How can you represent any rational number as a fraction?
Because a rational number is DEFINED as a number which can be expressed in that form!
Why is the quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
Is 3.245245245 a rational number?
Assuming that the number ends at that third 5, yes, the number is rational - as it has a defined end-point. If the number is equal to 3.245 recurring, then no, the number will not be rational.
