Rational numbers
Rational Numbers
Rational Numbers is a topic in Numbers & Operations in the California Common Core State Standards. It is aligned to Standard 6.NS.6, which requires students to recognize rational numbers and represent them as fractions and decimals.
A rational number can be written as a fraction \(\dfrac{a}{b}\) of integers with \(b\neq0\), including terminating and repeating decimals.
Theory
A rational number is any number that can be written as \(\dfrac{a}{b}\) where \(a\) and \(b\) are integers and \(b\neq0\).
Definition:
How to recognize a rational number
- Check if it can be written as a fraction of integers.
- Decimals that terminate or repeat qualify.
- Integers qualify (denominator \(1\)).
- Compare by using a common denominator.
Yes — it equals \(\dfrac{3}{4}\).
| \(0.75\) | \(=\) | \(\dfrac{3}{4}\) |
Yes — it equals \(\dfrac{1}{3}\).
| \(0.\overline{3}\) | \(=\) | \(\dfrac{1}{3}\) |
Yes — \(-5=\dfrac{-5}{1}\).
| \(-5\) | \(=\) | \(\dfrac{-5}{1}\) |
Common denominator \(15\): \(\dfrac{10}{15}\) vs \(\dfrac{9}{15}\).
| \(\dfrac{2}{3}\) | \(>\) | \(\dfrac{3}{5}\) |
Common pitfalls
Frequently asked questions
What is a rational number?
Any number writable as a fraction of two integers with a nonzero denominator.
Are decimals rational?
Yes, if they terminate or repeat.
Is every integer rational?
Yes.
Can the denominator be zero?
No.