The idea
Equivalent fractions have the same value because their numerator and denominator are multiplied or divided by the same non-zero number. A fraction in lowest terms has a terminating decimal precisely when its denominator has no prime factors other than 2 and 5. Other fractions have recurring decimal expansions.
Worked example
Write 0.375 as a fraction in its simplest form, then write 3/8 as a percentage.
- 0.375 = 375/1000.
- Divide numerator and denominator by 125 to get 3/8.
- 3/8 = 0.375, and multiplying by 100 gives 37.5%.
A mistake to avoid
Divide both the numerator and denominator when simplifying. Changing only one changes the value of the fraction.
Check your understanding
Write 0.06 as a fraction in simplest form.
Show the explanation
0.06 = 6/100 = 3/50.
Explore the lesson
This guide connects to Fractions and Decimals in the IGCSE Mathematics course. The first two published lessons per subject are free previews; further interactive lessons require an account.