Ordering Numbers Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
Order from least to greatest: 38\frac{3}{8}, 0.40.4, 13\frac{1}{3}, 0.3750.375.

Solution

  1. 1
    Convert all values to decimals for easy comparison: 38=0.375\frac{3}{8} = 0.375, 0.4=0.4000.4 = 0.400, 13≈0.333\frac{1}{3} \approx 0.333, 0.375=0.3750.375 = 0.375.
  2. 2
    Compare the decimal values: 0.333<0.375=0.375<0.4000.333 < 0.375 = 0.375 < 0.400.
  3. 3
    Write in original form from least to greatest: 13,  38=0.375,  0.4\frac{1}{3},\; \frac{3}{8} = 0.375,\; 0.4. Note that 38\frac{3}{8} and 0.3750.375 are equal.

Answer

13<38=0.375<0.4\frac{1}{3} < \frac{3}{8} = 0.375 < 0.4
Converting fractions and decimals to a common format (all decimals) makes ordering straightforward. Notice that 38\frac{3}{8} and 0.3750.375 are the same value. When comparing, align decimal places and compare digit by digit from left to right.

About Ordering Numbers

Ordering numbers is the process of arranging numbers in sequence from smallest to largest (ascending order) or largest to smallest (descending order). To order numbers, compare them using place value, common denominators, or convert to the same form (e.g. all decimals).

Learn more about Ordering Numbers →

More Ordering Numbers Examples

Example 1 easy

Arrange from least to greatest: [formula], [formula], [formula], [formula].

Example 2 medium

Order from greatest to least: [formula], [formula], [formula], [formula].

Example 4 easy

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

Example 5 medium

Insert a rational number between [formula] and [formula].

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