Ordering Numbers Examples in Math

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

Arranging a collection of numbers from least to greatest (ascending) or greatest to least (descending).

Numbers live on a line—you can always put them in order from left to right.

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: Every pair of real numbers can be compared; no two different numbers are 'equal' in order.

Common stuck point: Ordering negative numbers (bigger magnitude = smaller value).

Sense of Study hint: Draw a quick number line, plot each number as a dot, then read them off from left to right for least to greatest.

Worked Examples

Example 1

easy
Arrange from least to greatest: \frac{1}{2}, 0.3, \frac{3}{4}, 0.65.

Solution

  1. 1
    Convert all to decimals: \frac{1}{2} = 0.5, 0.3 = 0.3, \frac{3}{4} = 0.75, 0.65 = 0.65.
  2. 2
    Order the decimals: 0.3 < 0.5 < 0.65 < 0.75.
  3. 3
    In original form: 0.3 < \frac{1}{2} < 0.65 < \frac{3}{4}.

Answer

0.3 < \frac{1}{2} < 0.65 < \frac{3}{4}
To order a mixed set of fractions and decimals, convert everything to the same format (decimals are easiest) and compare. Then translate back to the original representations for the answer.

Example 2

medium
Order from greatest to least: -\frac{1}{2}, -0.6, 0, -\frac{1}{3}.

Example 3

medium
Order from least to greatest: \frac{3}{8}, 0.4, \frac{1}{3}, 0.375.

Practice Problems

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

Example 1

easy
Write three integers in order such that each is exactly 5 less than the previous.

Example 2

medium
Insert a rational number between \frac{2}{5} and \frac{3}{5}.
← Back to Ordering Numbers Formula Explained Practice Mode

Background Knowledge

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

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