What is a rational number?
A rational number is any number that can be written as a fraction a⁄b, where a and b are integers and b ≠ 0. This includes all integers (5 = 5⁄1), all fractions (−2⁄3), and all terminating or recurring decimals (0.25, 0.333…).
Key idea / Key idea
A number is rational if it equals a⁄b with integers a, b and b ≠ 0. Positive and negative integers, fractions and decimals that stop or repeat are all rational numbers.
Working with rational numbers
All the sign rules and BODMAS you learned still apply. It often helps to convert everything to the same form — usually fractions — before calculating.
Worked example / Worked example
Calculate −0.5 + 3⁄4.
Write −0.5 as a fraction: −0.5 = −1⁄2 = −2⁄4.
Then −2⁄4 + 3⁄4 = 1⁄4.
Converting between forms
To change a fraction to a decimal, divide the numerator by the denominator. To change a terminating decimal to a fraction, write it over a power of 10 and simplify. Being able to switch between forms lets you compare a fraction and a decimal quickly by putting them both into whichever form is easier.
- 3⁄8 = 3 ÷ 8 = 0.375
- 0.6 = 6⁄10 = 3⁄5
Remember / Remember
- Every integer is a rational number.
- b can never be 0 in a⁄b.
- Convert to a common form before combining.