Rational numbers
- Rational number
- A number that can be written as a fraction where and are integers and .
Whole numbers, fractions and terminating decimals are all rational. So are recurring decimals, where a digit or group of digits repeats forever. For example and
Irrational numbers
An irrational number cannot be written as a fraction of integers. Its decimal never ends and never repeats. Examples are and
Try itSquare-root explorer
Pick a whole number and see its square root on the number line. The last output tells you how far the root is from a whole number: 0 means a perfect square.
| Number | Rational or irrational? | Why |
|---|---|---|
| 0.75 | Rational | = 3/4 |
| √9 | Rational | = 3 |
| √5 | Irrational | 5 is not a perfect square |
| π | Irrational | never ends, never repeats |
Worked exampleChange a decimal to a fraction
Write as a fraction in its simplest form.
- Three decimal places means thousandths.
- Divide top and bottom by 125.
Answer:
Key terms
- Rational number
- A number that can be written as a fraction of integers.
- Irrational number
- A number whose decimal never ends or repeats.
- Recurring decimal
- A decimal where digits repeat forever.
- Perfect square
- A number that is the square of a whole number.
Summary
- Rational numbers are fractions of integers, including terminating and recurring decimals.
- Irrational numbers like √2 and π have decimals that never end or repeat.
- √n is rational only when n is a perfect square.