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.
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
- 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.
- Mixed Number → Decimal: Keep the whole number. Divide the fraction’s numerator by its denominator. Write the result after the decimal point.
- 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.
- \(\color{blue}{1.5}\) (decimal to mixed number)
- \(\color{blue}{5.25}\) (decimal to mixed number)
- \(\color{blue}{7.8}\) (decimal to mixed number)
- \(\color{blue}{3 \frac{1}{4}}\) (mixed number to decimal)
- \(\color{blue}{6 \frac{3}{8}}\) (mixed number to decimal)
- \(\color{blue}{4 \frac{2}{5}}\) (mixed number to decimal)
Answers
- \(\color{blue}{1 \frac{1}{2}}\)
- \(\color{blue}{5 \frac{1}{4}}\)
- \(\color{blue}{7 \frac{4}{5}}\)
- \(\color{blue}{3.25}\) (\(\color{blue}{1 \div 4 = 0.25}\); add 3)
- \(\color{blue}{6.375}\) (\(\color{blue}{3 \div 8 = 0.375}\); add 6)
- \(\color{blue}{4.4}\) (\(\color{blue}{2 \div 5 = 0.4}\); add 4)
Frequently Asked Questions
What is the difference between a mixed number and an improper fraction?
A mixed number combines a whole number and a proper fraction (e.g., \(\color{blue}{3 \frac{1}{2}}\)). An improper fraction has a numerator larger than the denominator (e.g., \(\color{blue}{\frac{7}{2}}\)). Both represent the same value; \(\color{blue}{3 \frac{1}{2} = \frac{7}{2}}\).
What if the decimal part results in a repeating decimal when converting a mixed number?
Write the answer with a repeating bar. For example, \(\color{blue}{3 \frac{1}{3}}\): \(\color{blue}{1 \div 3 = 0.&\#773;3}\), so the decimal is \(\color{blue}{3.&\#773;3}\).
Why do these conversions matter on the GED?
GED problems often give values in one form and require calculations in another. Being able to switch between decimals and mixed numbers quickly keeps your arithmetic consistent and reduces errors.
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