Fraction to Decimal Converter
Convert fractions and mixed numbers to decimal form with step-by-step solutions
Convert Fraction to Decimal
Top part of the fraction
Bottom part of the fraction
Number of decimal places to show
Input Fraction
Decimal Conversion
Fraction Details:
Step-by-Step Solution
Common Fraction to Decimal Conversions
Terminating Decimals
Repeating Decimals
Conversion Methods
Division Method
Divide numerator by denominator: n ÷ d
Equivalent Fraction
Convert to power of 10 denominator
Long Division
Step-by-step division process
Types of Decimals
Terminating
Decimal ends after finite digits
Example: 1/4 = 0.25
Repeating
Decimal has repeating pattern
Example: 1/3 = 0.(3) = 0.333...
Mixed Repeating
Non-repeating then repeating
Example: 1/6 = 0.1(6) = 0.1666...
Tips & Notation
Parentheses indicate repeating digits: 0.(3) = 0.333...
Mixed numbers are converted to improper fractions first
Fractions are simplified before conversion
Terminating decimals have denominators with only factors of 2 and 5
Understanding Fraction to Decimal Conversion
What Are Fractions and Decimals?
Fractions and decimals are different ways to represent the same numbers. A fraction shows a part of a whole using a numerator (top) and denominator (bottom), while decimals use place values after a decimal point.
Conversion Process
- •Step 1: Simplify the fraction if possible
- •Step 2: Divide numerator by denominator
- •Step 3: Identify if decimal terminates or repeats
Decimal Classification
Terminating Decimals
Occur when the denominator (in lowest terms) has only prime factors of 2 and 5
Examples: 1/2, 3/4, 7/8, 1/5, 3/10
Repeating Decimals
Occur when the denominator has prime factors other than 2 and 5
Examples: 1/3, 2/7, 5/11, 1/6
Long Division Method
Systematic division to find exact decimal representation
Reveals repeating patterns in non-terminating decimals
Practical Applications
Measurement & Construction
Converting fractional measurements to decimal for precision tools
Finance & Commerce
Converting fractional currency, interest rates, and percentages
Science & Engineering
Precise calculations requiring decimal representation
Understanding Notation
Repeating Decimal Notation
- • 0.(3) means 0.333333... (3 repeats)
- • 0.1(6) means 0.1666... (6 repeats)
- • 0.(142857) means 0.142857142857... (entire sequence repeats)
Mixed Number Conversion
- • 2¾ = 2 + ¾ = 2 + 0.75 = 2.75
- • 3⅓ = 3 + ⅓ = 3 + 0.(3) = 3.(3)
- • First convert to improper fraction, then to decimal