Fraction to Decimal Converter: The Ultimate Guide
Converting a fraction to a decimal is a fundamental math skill used in everyday life, from cooking to construction. Whether you’re a student, teacher, or professional, understanding this conversion is essential.
How to Convert Fraction to Decimal
Here are three reliable methods to convert any fraction into a decimal:
Method #1: Expand the Denominator to a Power of 10
This method works best when the denominator can be easily multiplied to become 10, 100, 1000, etc.
- Step 1: Find a number that, when multiplied by the denominator, gives a power of 10 (10, 100, 1000).
- Step 2: Multiply both the numerator and the denominator by this number.
- Step 3: Write down the numerator with the decimal point placed according to the number of zeros in the denominator.
Examples:
- Example #1: Convert $\frac{3}{5}$
- Target denominator: 10 (since $5 \times 2 = 10$)
- Multiply numerator and denominator by 2:$$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$$
- Result: 0.6
- Example #2: Convert $\frac{3}{4}$
- Target denominator: 100 (since $4 \times 25 = 100$)
- Multiply numerator and denominator by 25:$$\frac{3 \times 25}{4 \times 25} = \frac{75}{100}$$
- Result: 0.75
- Example #3: Convert $\frac{5}{8}$
- Target denominator: 1000 (since $8 \times 125 = 1000$)
- Multiply numerator and denominator by 125:$$\frac{5 \times 125}{8 \times 125} = \frac{625}{1000}$$
- Result: 0.625
Method #2: Use a Calculator (Simple Division)
The fastest way to convert a fraction to a decimal is simple division. Just divide the top number (numerator) by the bottom number (denominator).
- For Proper/Improper Fractions:
- Example #1: Convert $\frac{2}{5}$$$2 \div 5 = \mathbf{0.4}$$
- For Mixed Numbers:
- Keep the integer (whole number) as is, and divide the fraction part. Then add them together.
- Example #2: Convert $1 \frac{2}{5}$
- Integer: 1
- Fraction: $2 \div 5 = 0.4$
- Total: $1 + 0.4 = \mathbf{1.4}$
Method #3: Long Division
If you don’t have a calculator, long division is the standard manual method.
- Example: Calculate $\frac{3}{4}$
- Set up the division: $3 \div 4$.
- Since 4 doesn’t go into 3, add a decimal point and a zero to make it 3.0.
- 4 goes into 30 seven times ($4 \times 7 = 28$), with a remainder of 2.
- Bring down another zero to make it 20.
- 4 goes into 20 five times ($4 \times 5 = 20$), with no remainder.
- Result: 0.75
| Fraction | Decimal |
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 2/3 | 0.666… |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
| 1/10 | 0.1 |
Frequently Asked Questions (FAQs)
- Q: What is a fraction to decimal converter?
- A: It is a tool or mathematical process used to transform a fraction (representing a part of a whole) into its decimal equivalent.
- Q: How do I turn a fraction into a decimal without a calculator?
- A: You can use the long division method (dividing the numerator by the denominator) or the “power of 10” method if the denominator is compatible.
- Q: What do I do with repeating decimals?
- A: Some fractions, like 1/3, result in repeating decimals (0.333…). You can round them to a specific decimal place (e.g., 0.33) or use a bar notation over the repeating digit.
Recommended Resources
- Khan Academy: Offers excellent video tutorials and practice exercises on converting fractions to decimals.
- Math is Fun: Provides easy-to-understand explanations and interactive examples.
- WolframAlpha: A powerful computational engine that can solve complex fraction conversions and provide step-by-step solutions.