Rational Numbers Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Rational Numbers.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Numbers that can be expressed as a ratio of two integers (\frac{a}{b} where b \neq 0).

Any number you can write as a fraction, including decimals that end or repeat.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Rationals fill in the gaps between integers on the number line.

Common stuck point: Not recognizing that different forms (\frac{1}{2}, 0.5, 50\%) are the same number.

Sense of Study hint: Try converting to the same form — write both as decimals or both as fractions to see if they match.

Worked Examples

Example 1

easy
Place the following numbers in order from least to greatest: \frac{3}{4}, 0.6, \frac{7}{10}.

Solution

  1. 1
    Convert all to decimals: \frac{3}{4} = 0.75, 0.6 = 0.6, \frac{7}{10} = 0.7.
  2. 2
    Order the decimals: 0.6 < 0.7 < 0.75.
  3. 3
    In original form: 0.6 < \frac{7}{10} < \frac{3}{4}.

Answer

0.6 < \frac{7}{10} < \frac{3}{4}
To compare rational numbers in different forms, convert them all to the same representation—usually decimals—then order them. Every rational number can be expressed as a terminating or repeating decimal.

Example 2

medium
Express 0.\overline{36} as a fraction in simplest form.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Which is greater: \frac{5}{8} or \frac{3}{5}?

Example 2

medium
Order these numbers from least to greatest: -\frac{1}{2}, -0.45, -\frac{3}{5}.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdecimalsintegers