Sonia is creating a visual diagram to show the relationship between rational numbers and whole numbers. She draws it to show that some whole numbers are rational numbers and some are not. Is this correct? Explain why or why not
All numbers are rational right?
no. all whole numbers are rational (fractions with denominator=1, as in 2/1, 4/1, etc.)
There are lots of numbers that are not rational (irrational), like π, √3, ∛5, etc. They cannot be expressed as the ratio of two integers.
No, all numbers are not rational. Rational numbers are numbers that can be expressed as a fraction, where both the numerator and denominator are integers. Whole numbers, on the other hand, are positive integers including zero.
To determine if an entire set of numbers is rational, we need to consider the definition of rational numbers. If every number in the set can be expressed as a fraction, then the set is a subset of rational numbers.
In the case of whole numbers, some of them can be expressed as fractions, while others cannot. For example, the number 5 can be expressed as 5/1, where both the numerator and denominator are integers. Therefore, 5 is a rational number. On the other hand, the number 0 cannot be expressed as a fraction with a non-zero denominator, as any non-zero number divided by 0 is undefined. Therefore, 0 is not a rational number.
So, Sonia's visual diagram is correct in showing that some whole numbers (such as 5) are rational numbers, while others (such as 0) are not.