Fraction to Decimal Calculator
Convert fractions to decimals with long division steps
How to Convert Fractions to Decimals
Converting fractions to decimals is done through division. The numerator is divided by the denominator using long division, which may result in either a terminating or repeating decimal.
Long Division Method
- Divide the numerator by the denominator
- Find the whole number part (if any)
- Calculate the remainder
- Multiply the remainder by 10 and divide again
- Repeat until remainder is 0 (terminating) or pattern repeats (repeating)
Example: Converting 3/4
- 3 ÷ 4 = 0 with remainder 3
- 30 ÷ 4 = 7 with remainder 2
- 20 ÷ 4 = 5 with remainder 0
- Result: 0.75 (terminating decimal)
Terminating vs Repeating Decimals
Terminating: Fractions with denominators containing only factors of 2 and/or 5 (like 1/4, 3/8, 7/20)
Repeating: Fractions with denominators containing other prime factors (like 1/3, 5/6, 2/7)
Frequently Asked Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator using long division. For example, to convert 3/4, divide 3 by 4, which equals 0.75.
What is 1/3 as a decimal?
1/3 equals 0.333... (repeating). The 3 repeats infinitely, so it's written as 0.3̄ or 0.(3) to indicate the repeating pattern.
How do you know if a fraction will be a terminating decimal?
A fraction in simplest form will be a terminating decimal if its denominator contains only the prime factors 2 and/or 5. For example, 1/4 (4=2²), 3/8 (8=2³), and 7/20 (20=2²×5) are all terminating.
What does repeating decimal mean?
A repeating decimal has one or more digits that repeat infinitely. For example, 1/3 = 0.333... where 3 repeats, and 1/7 = 0.142857142857... where 142857 repeats.
Can improper fractions be converted to decimals?
Yes, improper fractions (where numerator is larger than denominator) can be converted to decimals the same way. The result will be greater than 1. For example, 5/4 = 1.25.
What is long division?
Long division is a method for dividing large numbers step by step. When converting fractions, you divide the numerator by the denominator, bringing down zeros to continue the division until you get a remainder of 0 or a repeating pattern.