Fraction to Decimal Converter
Convert a fraction to an exact decimal and a percent. The tool reduces first, then uses long division so you can see whether the decimal terminates or repeats.
3/4 = 0.75
- Reduce 3/4. GCF is 1, so the fraction is already in lowest terms.
- Divide 3 by 4.
- The decimal terminates: 0.75.
- Percent: 0.75 × 100 = 75%.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Fraction to Decimal Converter
Enter a whole-number numerator and a nonzero whole-number denominator. Select Convert to Decimal or press Enter. The converter reduces the fraction, divides the terms, and reports a terminating decimal, a repeating block in parentheses, or an exact whole number.
- Type the numerator, including a negative sign if the value is below zero.
- Type a denominator other than zero.
- Read the decimal, the percent, the reduced fraction, and the long-division steps.
The work stays in your browser. The tool accepts proper fractions, improper fractions, negative terms, and a zero numerator. A negative denominator is flipped so the final sign sits on the numerator. Extremely large values outside JavaScript’s safe integer range are rejected so the arithmetic stays exact.
What does a/b as a decimal mean?
A fraction is a division problem. The decimal is the quotient of that division. 1/2 means one divided by two, which is 0.5. 2/5 means two divided by five, which is 0.4. The fraction and the decimal name the same point on the number line.
When should you keep the fraction?
Keep the fraction when you need an exact value through later arithmetic. 1/3 is exact. 0.333… is a repeating expansion of the same number. If you round too early, later steps drift. Convert to a decimal when you need a calculator display, a measurement readout, or a percent.
How to Convert a Fraction to a Decimal
Step 1: reduce the fraction
Find the greatest common factor of the numerator and denominator, then divide both terms by that factor. 18/24 reduces by 6 to 3/4. Reduction does not change the value. It only makes the later division shorter.
Step 2: divide numerator by denominator
If the remainder becomes zero, the decimal terminates. 3 ÷ 4 gives 0.75 and then stops. If a remainder repeats, the decimal repeats from the digit where that remainder first appeared.
Long division and remainders
Write the numerator under the division bracket and the denominator outside. Bring down zeros after the decimal point. Each new remainder is a leftover that has not yet been divided. When a leftover matches an earlier leftover, the digit sequence between those two remainders will loop forever.
For 1 ÷ 3 the first remainder after bringing down a zero is 10. 3 goes into 10 three times, leaving remainder 1. That is the same remainder you started with, so the digit 3 repeats: 0.(3).
Parentheses notation
This page writes a repeating block in parentheses. 1/3 = 0.(3). 1/6 = 0.1(6). 1/7 = 0.(142857). The digits outside the parentheses appear once. The digits inside the parentheses repeat without end. A bar over the repeating digits is the same idea.
Percent form
A percent is a decimal times 100. 3/4 = 0.75 = 75%. 1/8 = 0.125 = 12.5%. 1/3 = 0.(3) = 33.(3)%. The fraction remains the exact source. The percent is just another place-value reading of the same ratio.
Worked Fraction-to-Decimal Examples
Terminating hundredth: 3/4
GCF(3, 4) is 1, so the fraction is already reduced. 4 goes into 30 seven times (28), remainder 2. Bring down a zero to make 20. 4 goes into 20 five times exactly. The decimal is 0.75, and the percent is 75%.
Terminating eighth: 1/8
1 ÷ 8 = 0.125. Three decimal places appear because 8 = 2³, and every factor of 2 or 5 in the reduced denominator produces a terminating expansion. 0.125 × 100 = 12.5%.
Repeating third: 1/3
1 ÷ 3 never finishes. Each step produces remainder 1 and digit 3. The exact decimal is 0.(3). The percent is 33.(3)%. Writing only 0.33 is a rounded estimate, not the full value.
Mixed repeating: 1/6
1/6 reduces already. The first decimal digit is 1 and does not repeat. The next remainder loops on 6. The exact form is 0.1(6), which is 0.1666… The percent is 16.(6)%.
Six-digit cycle: 1/7
1/7 produces the famous block 142857. The decimal is 0.(142857). Multiples of 1/7 rotate that same block: 2/7 = 0.(285714), 3/7 = 0.(428571).
Improper fraction: 22/7
22 ÷ 7 is 3 with remainder 1, so the integer part is 3 and the decimal part is the 1/7 cycle. 22/7 = 3.(142857). This is a common rational stand-in for π, not π itself.
Already a whole number: 8/2
GCF(8, 2) is 2, so 8/2 reduces to 4/1. The decimal is simply 4. The percent is 400%. No decimal point is required.
Negative fraction: −5/8
Divide the magnitudes first: 5 ÷ 8 = 0.625. Attach the negative sign to the complete value: −0.625, or −62.5%. A negative denominator is normalized the same way, so 5/−8 also becomes −0.625.
Terminating Decimals and Repeating Decimals
After the fraction is in lowest terms, look only at the denominator. If that denominator’s prime factors are limited to 2 and 5, the decimal terminates. 1/2, 1/4, 1/5, 1/8, 1/10, 1/16, and 1/25 all terminate. If any other prime remains, such as 3, 7, 11, or 13, the decimal repeats.
| Fraction | Lowest terms | Decimal | Type |
|---|---|---|---|
| 1/2 | 1/2 | 0.5 | Terminating |
| 2/8 | 1/4 | 0.25 | Terminating |
| 3/5 | 3/5 | 0.6 | Terminating |
| 2/3 | 2/3 | 0.(6) | Repeating |
| 5/6 | 5/6 | 0.8(3) | Repeating |
| 2/7 | 2/7 | 0.(285714) | Repeating |
Every repeating decimal is still a rational number. It can be written as a fraction. The reverse page, the Decimal to Fraction Calculator, turns 0.75 into 3/4 and 0.(3) into 1/3. The two tools are inverses of the same relationship.
Why 1/3 is not 0.33
0.33 is 33/100. That is close to 1/3 but not equal. Cross-multiply to check: 1 × 100 = 100 and 3 × 33 = 99. The products differ, so the values differ. The repeating form 0.(3) is the exact expansion.
Place value and percent
0.75 means 7 tenths and 5 hundredths, which is 75 hundredths, which is 75%. 0.125 means 125 thousandths, which is 12.5%. Moving the decimal point two places to the right converts any decimal into a percent without changing the underlying ratio.
Common Fraction-to-Decimal Mistakes
Dividing the denominator by the numerator
The fraction bar means numerator divided by denominator. 3/4 is 3 ÷ 4 = 0.75, not 4 ÷ 3.
Stopping a repeating decimal too soon
0.33 is a rounded stand-in for 1/3. Keep the repeating block, or keep the fraction, when you need the exact value.
Forgetting to reduce first
18/24 and 3/4 have the same decimal. Reducing first makes the long division shorter and the GCF visible.
Treating 0.75 as 75/10
Two digits after the decimal are hundredths, so 0.75 = 75/100 = 3/4. Use the Decimal to Fraction Calculator if you are going in that direction.
Writing a percent without multiplying by 100
3/4 is 0.75, not 75, until you convert to a percent. The percent is 75%.
Allowing a zero denominator
Division by zero is undefined. A fraction with denominator 0 cannot become a decimal.
Dropping the negative sign
The sign belongs to the complete value. −3/4 = −0.75, not 0.75.
How to Check a Fraction-to-Decimal Result
Multiply the decimal by the original denominator. You should recover the original numerator when the decimal is exact. 0.75 × 4 = 3, so 3/4 checks. For a repeating decimal, convert back with nines in the denominator: 0.(3) = 3/9 = 1/3.
You can also convert the decimal back on the Decimal to Fraction Calculator and compare lowest terms. If both tools return the same reduced fraction, the pair is consistent.
Safe integer scope
This converter is built for classroom, homework, and everyday whole-number terms inside JavaScript’s safe integer range. It is not a computer-algebra system. Very large numerators should be handled with arbitrary-precision software.
Related learning path
Use the Fraction Calculator to add, subtract, multiply, or divide two fractions. Use the Simplify Fraction Calculator when you only need lowest terms. Use the Decimal to Percent Calculator when you already have a decimal and want the percent only.
Fraction to Decimal Converter FAQs
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. Reduce first if you want shorter steps. 3/4 becomes 3 ÷ 4 = 0.75.
How do I convert 1/3 to a decimal?
1 ÷ 3 repeats. The exact decimal is 0.(3), also written 0.333…
What do the parentheses in 0.(3) mean?
They mark the repeating block. 0.(3) means 0.333… and 0.1(6) means 0.1666…
How do I convert a fraction to a percent?
Convert to a decimal, then multiply by 100. 3/4 = 0.75 = 75%.
Can the converter handle improper fractions?
Yes. 22/7 becomes 3.(142857). The integer part is the whole number of times the denominator divides the numerator.
Why can the denominator not be zero?
Division by zero is undefined, so a zero denominator cannot represent a fraction or a decimal.
Are my numbers sent to a server?
No. The conversion runs locally in your browser.
Related Fraction Calculators
Explore More Fraction Tools
Continue with fraction, decimal, and percent tools in the SolverCalc fractions collection.
Browse Fraction ToolsReviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.