Rational Numbers
11-2Decimal Forms of Rational Numbers
Overview
Every rational number has either a terminating or a repeating decimal expansion.
Key ideas
- Terminating decimals come from denominators with only 2s and 5s.
- Otherwise the decimal repeats.
- A bar over digits marks the repeat block.
Worked examples
Example 1
Problem. Decimal of 3/4.
Solution. 0.75 (terminating)
Example 2
Problem. Decimal of 1/3.
Solution. 0.333… = 0.3̄
Practice
Try each one. Click Show answer when ready.
- 1.
Decimal of 5/8.
- 2.
Decimal of 2/9.
- 3.
Decimal of 7/20.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Express 5/11 as a decimal.
- 2.
Express 7/12 as a decimal.