Lesson 4: Decimal Representation of Rational and Irrational Numbers

Property

We can find the decimal form for any fraction by dividing the denominator into the numerator.
Remember that the fraction bar is really a division symbol.
For instance, $\frac{1}{4}$ means "divide one whole into four equal parts," or $1 \div 4 = 0.25$.

Benchmark Fractions as Decimals:

Examples

• To find the decimal form of $\frac{1}{8}$, we calculate $1 \div 8$, which equals $0.125$.
• The decimal form of the fraction $\frac{2}{5}$ is found by dividing 2 by 5, which gives $2 \div 5 = 0.4$.
• For the fraction $\frac{9}{20}$, we perform the division $9 \div 20$, which results in $0.45$.

Property

A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.

1. The decimal representation terminates, or ends.

2. The decimal representation repeats a pattern.

Property

A rational number has a decimal representation that either terminates (ends) or repeats a pattern.

An irrational number has a decimal representation that is non-terminating and non-repeating.