Decimal to Fraction Calculator
Convert decimals to fractions with step-by-step solutions
How to Convert Decimals to Fractions
Converting decimals to fractions involves understanding place values and simplification. The process varies slightly depending on whether the decimal is terminating or repeating.
Method for Terminating Decimals
- Count the number of decimal places in the number
- Write the decimal as a fraction with denominator 10, 100, 1000, etc.
- Find the greatest common divisor (GCD) of numerator and denominator
- Divide both numerator and denominator by the GCD to simplify
- Convert to mixed number if the fraction is improper (optional)
Example: Converting 0.75
- 0.75 has 2 decimal places
- Write as 75/100
- GCD of 75 and 100 is 25
- 75 ÷ 25 = 3, 100 ÷ 25 = 4
- Result: 3/4
Common Decimal to Fraction Conversions
Frequently Asked Questions
How do you convert a decimal to a fraction?
Count the decimal places, write the number as a fraction with a power of 10 as the denominator, then simplify by dividing both numerator and denominator by their greatest common divisor.
What is 0.5 as a fraction?
0.5 equals 1/2. Since 0.5 has one decimal place, it becomes 5/10, which simplifies to 1/2 when divided by 5.
Can all decimals be converted to fractions?
All terminating and repeating decimals can be converted to fractions. Non-repeating, non-terminating decimals (like π) cannot be expressed as exact fractions.
What is the difference between terminating and repeating decimals?
Terminating decimals have a finite number of digits (like 0.75), while repeating decimals have digits that repeat infinitely (like 0.333...). Both can be converted to fractions using different methods.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by this number. For example, 75/100 has a GCD of 25, so it simplifies to 3/4.
What is an improper fraction vs a mixed number?
An improper fraction has a numerator larger than its denominator (like 7/4). A mixed number combines a whole number with a proper fraction (like 1 3/4). Both represent the same value.