Convert Between Decimals and Mixed Numbers

Converting between decimals and mixed numbers is a key skill for the GED Mathematical Reasoning test. Mixed numbers and decimals represent the same values in different forms, and being fluent in both directions lets you compare quantities, solve equations, and interpret real-world measurements with confidence.

What Are Decimals and Mixed Numbers?

A decimal like \(\color{blue}{2.5}\) has a whole-number part (2) and a fractional part (0.5) separated by a decimal point. A mixed number like \(\color{blue}{2 \frac{1}{2}}\) expresses the same value as a whole number and a proper fraction. Converting between them is simply a matter of recognizing and rewriting the fractional part.

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How to Convert a Decimal to a Mixed Number

Step 1: Identify the whole-number part

The digits to the left of the decimal point form the whole number.

Step 2: Convert the decimal part to a fraction

Write the decimal digits over the appropriate power of 10, then simplify.

• \(\color{blue}{2.5}\): \(\color{blue}{\text{ whole } = 2}\); decimal part = \(\color{blue}{0.5 = \frac{5}{10} = \frac{1}{2}}\). Mixed number: \(\color{blue}{2 \frac{1}{2}}\).
• \(\color{blue}{3.75}\): \(\color{blue}{\text{ whole } = 3}\); decimal part = \(\color{blue}{0.75 = \frac{75}{100} = \frac{3}{4}}\). Mixed number: \(\color{blue}{3 \frac{3}{4}}\).
• \(\color{blue}{1.25}\): \(\color{blue}{\text{ whole } = 1}\); decimal part = \(\color{blue}{0.25 = \frac{1}{4}}\). Mixed number: \(\color{blue}{1 \frac{1}{4}}\).
• \(\color{blue}{4.6}\): \(\color{blue}{\text{ whole } = 4}\); decimal part = \(\color{blue}{0.6 = \frac{3}{5}}\). Mixed number: \(\color{blue}{4 \frac{3}{5}}\).

How to Convert a Mixed Number to a Decimal

Convert the fractional part to a decimal

Divide the numerator of the fraction by its denominator, then add the whole number.

• \(\color{blue}{3 \frac{1}{2}}\): \(\color{blue}{1 \div 2 = 0.5}\); add 3 → \(\color{blue}{3.5}\).
• \(\color{blue}{2 \frac{3}{4}}\): \(\color{blue}{3 \div 4 = 0.75}\); add 2 → \(\color{blue}{2.75}\).
• \(\color{blue}{5 \frac{1}{8}}\): \(\color{blue}{1 \div 8 = 0.125}\); add 5 → \(\color{blue}{5.125}\).

Step-by-Step Summary

1. Decimal → Mixed Number: Separate whole and decimal parts. Write the decimal part as a fraction over a power of 10. Simplify. Combine with the whole number.
2. Mixed Number → Decimal: Keep the whole number. Divide the fraction’s numerator by its denominator. Write the result after the decimal point.
3. Always simplify the fractional part to lowest terms.

Watch: Decimals to Mixed Numbers (Video Lesson)

Math with Mr. J explains how to convert decimals to mixed numbers including simplifying the fractional part:

Convert Between Decimals and Mixed Numbers – Worked Examples

Example 1: Convert \(\color{blue}{2.5}\) to a mixed number.

Whole part: 2. Decimal part: \(\color{blue}{0.5 = \frac{5}{10} = \frac{1}{2}}\).
Answer: \(\color{blue}{2 \frac{1}{2}}\).

Example 2: Convert \(\color{blue}{3.75}\) to a mixed number.

Whole part: 3. Decimal part: \(\color{blue}{0.75 = \frac{75}{100} = \frac{3}{4}}\).
Answer: \(\color{blue}{3 \frac{3}{4}}\).

Example 3: Convert \(\color{blue}{4 \frac{3}{5}}\) to a decimal.

Fraction part: \(\color{blue}{3 \div 5 = 0.6}\). Add whole number: \(\color{blue}{4 + 0.6 = 4.6}\).

Example 4: Convert \(\color{blue}{2.125}\) to a mixed number.

Whole part: 2. Decimal part: \(\color{blue}{0.125 = \frac{125}{1000} = \frac{1}{8}}\).
Answer: \(\color{blue}{2 \frac{1}{8}}\).

More Practice: Converting Mixed Numbers to Decimals (Video)

The Organic Chemistry Tutor demonstrates converting mixed numbers to decimals with clear examples:

Exercises

Convert each decimal to a mixed number and each mixed number to a decimal.

1. \(\color{blue}{1.5}\) (decimal to mixed number)
2. \(\color{blue}{5.25}\) (decimal to mixed number)
3. \(\color{blue}{7.8}\) (decimal to mixed number)
4. \(\color{blue}{3 \frac{1}{4}}\) (mixed number to decimal)
5. \(\color{blue}{6 \frac{3}{8}}\) (mixed number to decimal)
6. \(\color{blue}{4 \frac{2}{5}}\) (mixed number to decimal)

Answers

1. \(\color{blue}{1 \frac{1}{2}}\)
2. \(\color{blue}{5 \frac{1}{4}}\)
3. \(\color{blue}{7 \frac{4}{5}}\)
4. \(\color{blue}{3.25}\) (\(\color{blue}{1 \div 4 = 0.25}\); add 3)
5. \(\color{blue}{6.375}\) (\(\color{blue}{3 \div 8 = 0.375}\); add 6)
6. \(\color{blue}{4.4}\) (\(\color{blue}{2 \div 5 = 0.4}\); add 4)

Frequently Asked Questions

How do you convert between decimals and mixed numbers?

To go from a decimal to a mixed number, keep the digits left of the decimal point as the whole number and turn the decimal part into a simplified fraction: 3.75 becomes 3 and 75/100, or 3 3/4. To go the other way, divide the fraction’s numerator by its denominator and add the whole number: 4 2/5 = 4 + 0.4 = 4.4.

What is a mixed decimal?

A mixed decimal usually means a decimal that has both a whole-number part and a decimal part, such as 2.5 or 12.08. It is the decimal form of a mixed number, so 2.5 matches 2 1/2. A decimal less than 1, like 0.6, has no whole-number part and is not usually called a mixed decimal.

How do you convert decimals to mixed numbers?

Split the decimal at the point. The left side is the whole number. Write the right side over 10, 100 or 1000, depending on how many decimal places it has, then simplify. For 1.25, the whole number is 1 and 0.25 = 25/100 = 1/4, so 1.25 = 1 1/4. For 6.125, 0.125 = 125/1000 = 1/8, giving 6 1/8.

How do you convert mixed numbers to decimals?

Change only the fraction part to a decimal by dividing the numerator by the denominator, then put the whole number in front. For 5 3/8, 3 ÷ 8 = 0.375, so 5 3/8 = 5.375. Some fractions repeat, such as 2 1/3 = 2.333…, so you may need to round or show the repeat with a bar. A calculator can check your division.

How do you convert between decimals and fractions or mixed numbers?

If the decimal is less than 1, write it as a simple fraction, such as 0.6 = 6/10 = 3/5. If it is greater than 1, you can write either an improper fraction or a mixed number: 2.75 = 275/100 = 11/4, which is the same as 2 3/4. Choose whichever form the question asks for.

Related Topics

• Convert Between Fractions and Decimals
• Convert Between Improper Fractions and Mixed Numbers
• Simplifying Fractions
• Order of Decimals Mixed Numbers and Fractions
• Multiplying Mixed Numbers