How to Convert Decimals to Fractions
Learn how to convert decimals to fractions by place value, simplify fractions, handle repeating decimals, avoid mistakes, troubleshoot issues, and read FAQs.
Quick Answer
To convert a decimal to a fraction, write the decimal digits over the matching place value, then simplify. For example, 0.75 = 75/100 = 3/4.
What You Need
- Decimal number
- Place value knowledge
- Simplifying fractions
- Greatest common factor if needed
- Calculator for checking if allowed
Safety Precautions
- Count decimal places carefully.
- Do not forget to simplify the fraction.
- Handle repeating decimals differently from terminating decimals.
- Keep negative signs with the final fraction.
Step-by-Step Instructions
- Step 1
Read place value
Count how many digits are after the decimal point.
- Step 2
Write numerator
Use the decimal digits without the decimal point.
- Step 3
Write denominator
Use 10, 100, 1000, or another power of 10 based on decimal places.
- Step 4
Build fraction
Place numerator over denominator.
- Step 5
Simplify
Divide numerator and denominator by their greatest common factor.
- Step 6
Keep sign
If the decimal is negative, the fraction is negative.
- Step 7
Check
Divide the fraction to confirm it returns the decimal.
Practical Example
Example: 0.6 has one decimal place, so write 6/10, then simplify to 3/5.
Common Mistakes
- Using wrong denominator
- Forgetting to simplify
- Dropping a negative sign
- Treating repeating decimals like terminating decimals
- Miscounting zeros
- Rounding when exact answer is needed
Troubleshooting
Decimal has three places
Use denominator 1000 before simplifying.
Fraction is not simplified
Divide top and bottom by common factors.
Decimal repeats forever
Use a repeating-decimal method rather than simple place value.
Answer seems wrong
Divide numerator by denominator to check.
Helpful Internal Links
FAQs
What is 0.5 as a fraction?
0.5 = 5/10 = 1/2.
What is 0.25 as a fraction?
0.25 = 25/100 = 1/4.
What denominator do decimals use?
Use powers of 10, such as 10, 100, or 1000.
Do repeating decimals work the same way?
No, repeating decimals need a different algebraic method.
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