Rational Numbers: Is Any Whole Number a Rational?

In summary, whole numbers are a subset of rational numbers and can be expressed as an integer divided by another integer. Therefore, any whole number divided by any other whole number (except for 0) will result in a rational number.
  • #1
Justin Kirk
11
0
Are whole numbers rational numbers? If so, will any whole number divided by any other whole number result in a rational number?
 
Physics news on Phys.org
  • #2
A rational number, by definition, is an integer divided by another integer (that's not equal to zero).

As for the integers themselves, for example [tex]3=\frac{3}{1}[/tex] we see that 3 is in fact an integer divided by another integer, so is a rational number as well. The same exact argument can be used for any whole number
 
  • #3
Yes, the "whole numbers" is a subset of the rational numbers.

The answer to "will any whole number divided by any other whole number be a rational number" is "almost". Any whole number divided by any whole number except 0 is a rational number.
 

FAQ: Rational Numbers: Is Any Whole Number a Rational?

What is a rational number?

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. This includes both whole numbers and fractions.

Is every whole number a rational number?

Yes, every whole number is a rational number because it can be expressed as a ratio of itself and 1. For example, 5 can be written as 5/1, which is a ratio of two integers.

What is an example of a rational number that is not a whole number?

An example of a rational number that is not a whole number is 3/4. This fraction is not a whole number because it is a part of a whole, but it is still a rational number because it can be expressed as a ratio of two integers.

Can irrational numbers be expressed as rational numbers?

No, irrational numbers cannot be expressed as rational numbers. Irrational numbers are numbers that cannot be expressed as a ratio of two integers, such as pi or the square root of 2.

How do you determine if a number is rational or irrational?

To determine if a number is rational or irrational, you can try to express it as a fraction. If you can write the number as a ratio of two integers, then it is rational. If not, then it is irrational. Alternatively, you can also check if the number has a repeating or terminating decimal. If it does, then it is rational, and if it doesn't, then it is irrational.

Similar threads

Replies
6
Views
1K
Replies
33
Views
3K
Replies
4
Views
667
Replies
3
Views
2K
Replies
7
Views
1K
Replies
13
Views
4K
Back
Top