Question

I have a problem, it says, identify the set of numbers that best describes each situation. The situation is, the amount of money in a bank account. we are working with, real, rational, irrational, integers, and whole numbers. Is it irrational or rational? ​

Answer 1

Rational

Explanation:

We first have to define what these numbers mean:

Real numbers are all the numbers on the number line, they are not imaginary numbers that cannot be quantified on the number line.

Rational numbers are numbers that have either terminating decimals or recurring decimal, for example 5.3 (terminating decimal) or 1.333...(recurring decimal). I did not use the traditional definition of "a/b where a and b are integers and b ≠ 0" because it poses some problems. For instance 22/7 fulfills this condition but it is not a rational number! So it is best defined the way I just defined it.

An irrational number is a number that does not have terminating and recurring decimal, like 3.565215805.....

Integers are real numbers that are whole numbers.

Looking at the situation, which is the money in a bank account. The value will be a number that is rational because it is always an exact amount and this implies that it will always be a terminating decimal. Note that 45.00 is also a terminating decimal.