Order of Decimals, Mixed Numbers and Fractions

How to order of decimals, mixed numbers and fractions, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Ordering decimals, mixed numbers, and fractions together is a skill the GED Mathematical Reasoning test frequently assesses. When numbers appear in different forms, you must convert them to the same form before you can compare. The most reliable approach is to convert everything to a decimal, then arrange by value.

What Does It Mean to Order Decimals, Mixed Numbers, and Fractions?

To order a set of numbers means to arrange them from least to greatest (or greatest to least). When the numbers are in mixed forms, some as fractions, some as decimals, some as mixed numbers, the comparison is easiest if you first convert every number to the same format (typically a decimal) and then sort.

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How to Order Mixed Numbers, Fractions, and Decimals

Method 1: Convert all to decimals

Divide each fraction to get a decimal; bring down whole-number parts for mixed numbers. Then order the decimals.

• \(\color{blue}{\frac{3}{4} = 0.75}\)
• \(\color{blue}{0.5}\) stays as \(\color{blue}{0.5}\)
• \(\color{blue}{\frac{7}{8} = 0.875}\)
• \(\color{blue}{1.2}\) stays as \(\color{blue}{1.2}\)
• \(\color{blue}{\frac{5}{6} &\text{ approx }; 0.8&\#773;3}\)

Order: \(\color{blue}{0.5 < 0.75 < 0.8&\#773;3 < 0.875 < 1.2}\), so the original order from least to greatest is: \(\color{blue}{0.5, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}, 1.2}\).

Method 2: Convert all to fractions with a common denominator

This works well when all values are fractions or easily written as fractions. Find the LCD and compare numerators.

• Compare \(\color{blue}{\frac{2}{3}}\) and \(\color{blue}{\frac{3}{5}}\): \(\color{blue}{\text{ LCD } = 15}\). \(\color{blue}{\frac{2}{3} = \frac{10}{15}}\), \(\color{blue}{\frac{3}{5} = \frac{9}{15}}\). So \(\color{blue}{\frac{3}{5} < \frac{2}{3}}\).

Step-by-Step Summary

1. Convert all numbers to decimals (divide fractions; write decimal parts for mixed numbers).
2. Align decimal points and compare digit by digit from left to right.
3. Arrange in the required order (least to greatest or greatest to least).
4. Rewrite the answer using the original form of each number.

Watch: Ordering Decimals, Fractions, and Mixed Numbers (Video Lesson)

This lesson walks through converting and ordering numbers in mixed forms:

Worked Examples

Example 1: Order from least to greatest: \(\color{blue}{\frac{7}{8}, 0.5, 1 \frac{1}{5}, \frac{3}{4}}\).

Convert: \(\color{blue}{\frac{7}{8} = 0.875}\), \(\color{blue}{0.5}\), \(\color{blue}{1 \frac{1}{5} = 1.2}\), \(\color{blue}{\frac{3}{4} = 0.75}\).
Order decimals: \(\color{blue}{0.5 < 0.75 < 0.875 < 1.2}\).
Answer: \(\color{blue}{0.5, \frac{3}{4}, \frac{7}{8}, 1 \frac{1}{5}}\).

Example 2: Order from greatest to least: \(\color{blue}{0.6, \frac{5}{8}, \frac{2}{3}}\).

Convert: \(\color{blue}{0.6}\), \(\color{blue}{\frac{5}{8} = 0.625}\), \(\color{blue}{\frac{2}{3} &\text{ approx }; 0.&\#773;6 = 0.6666\ldots}\)
Order: \(\color{blue}{0.6666\ldots > 0.6 > 0.625}\).
Answer: \(\color{blue}{\frac{2}{3}, 0.6, \frac{5}{8}}\).

Example 3: Order from least to greatest: \(\color{blue}{1 \frac{3}{4}, 1.5, 1 \frac{2}{3}}\).

All are between 1 and 2. Fractional parts: \(\color{blue}{\frac{3}{4} = 0.75}\), \(\color{blue}{0.5}\), \(\color{blue}{\frac{2}{3} &\text{ approx }; 0.667}\).
Order of fractional parts: \(\color{blue}{0.5 < 0.667 < 0.75}\).
Answer: \(\color{blue}{1.5, 1 \frac{2}{3}, 1 \frac{3}{4}}\).

Example 4: Which is greatest: \(\color{blue}{0.8}\), \(\color{blue}{\frac{4}{5}}\), or \(\color{blue}{\frac{7}{9}}\)?

Convert: \(\color{blue}{0.8}\), \(\color{blue}{\frac{4}{5} = 0.8}\), \(\color{blue}{\frac{7}{9} &\text{ approx }; 0.&\#773;7 = 0.777\ldots}\)
\(\color{blue}{0.8 = \frac{4}{5} > \frac{7}{9}}\). Answer: \(\color{blue}{0.8 \text{ and } \frac{4}{5} \text{ are tied } (\text{ equal }); \text{ both are greater than } \frac{7}{9}}\).

More Practice: Compare and Order Fractions and Decimals (Video)

This video teaches multiple methods for comparing and ordering fractions and decimals:

Exercises

Order each set from least to greatest.

1. \(\color{blue}{\frac{3}{5}, 0.7, \frac{1}{2}}\)
2. \(\color{blue}{1 \frac{1}{4}, 1.3, 1 \frac{1}{3}}\)
3. \(\color{blue}{0.25, \frac{1}{3}, \frac{3}{8}}\)
4. \(\color{blue}{2.5, 2 \frac{1}{4}, 2 \frac{3}{8}}\)
5. \(\color{blue}{\frac{5}{6}, 0.75, \frac{7}{8}}\)
6. \(\color{blue}{\frac{1}{2}, 0.4, \frac{2}{5}, 0.45}\)

Answers

1. \(\color{blue}{\frac{1}{2} (0.5) < \frac{3}{5} (0.6) < 0.7}\)
2. \(\color{blue}{1 \frac{1}{4} (1.25) < 1 \frac{1}{3} (1.&\#773;3) < 1.3}\) — Note: \(\color{blue}{1.3 > 1.&\#773;3 &\text{ approx }; 1.333}\)? No: \(\color{blue}{1.333 > 1.3}\). Corrected: \(\color{blue}{1 \frac{1}{4} < 1.3 < 1 \frac{1}{3}}\).
3. \(\color{blue}{0.25 < \frac{1}{3} (0.&\#773;3) < \frac{3}{8} (0.375)}\)
4. \(\color{blue}{2 \frac{1}{4} (2.25) < 2 \frac{3}{8} (2.375) < 2.5}\)
5. \(\color{blue}{0.75 < \frac{5}{6} (0.8&\#773;3) < \frac{7}{8} (0.875)}\)
6. \(\color{blue}{\frac{2}{5} (0.4) = 0.4 < 0.45 < \frac{1}{2} (0.5)}\)

Frequently Asked Questions

How do you order decimals and fractions?

Convert every number to the same form, usually a decimal, and then compare. For 3/4, 0.7, 2/3 and 0.72, the decimals are 0.75, 0.7, about 0.667 and 0.72. From least to greatest, that is 2/3, 0.7, 0.72, 3/4. Write the original forms in your final answer, not just the decimals.

How do you order decimals from least to greatest?

Line the numbers up by their decimal points and add zeros so they have the same number of decimal places. Then compare digit by digit from the left. For 0.6, 0.58 and 0.605, rewrite them as 0.600, 0.580 and 0.605. The order from least to greatest is 0.58, 0.6, 0.605.

How do you order decimals on a number line?

Mark the whole numbers, divide the space between them into tenths or hundredths, and place each number. The one farthest left is the least. To order 1 3/5, 1.45 and 1 1/2, write them as 1.6, 1.45 and 1.5 and plot them between 1 and 2. Reading left to right gives 1.45, 1 1/2, 1 3/5.

Is there a calculator to order decimals?

Yes, online tools can sort a list of decimals, and any calculator can turn fractions into decimals by dividing. For a mixed number like 2 5/8, divide 5 by 8 to get 0.625, then add 2 to get 2.625. Doing the comparison yourself is still worth practicing, because tests often expect you to order numbers without a sorting tool.

Related Topics

• Convert Between Fractions and Decimals
• Convert Between Decimals and Mixed Numbers
• Convert Between Improper Fractions and Mixed Numbers
• Simplifying Fractions
• Using Number Lines to Represent Integers