Decimal to fraction calculator guide
Every terminating decimal is a fraction whose denominator is a power of ten: 0.75 is seventy-five hundredths, or 75/100, which reduces to 3/4. This calculator performs that conversion for you and returns the fraction in lowest terms.
Enter a decimal such as 0.375 or 1.75 and select Calculate. The result shows the improper fraction first; when the absolute value is one or greater, a mixed-number form is shown as well. Negative decimals are supported and keep their sign.
How to use the decimal to fraction calculator
- Enter the decimal: Type a decimal number such as 0.75, 2.5, or -0.375. A leading zero and a leading minus sign are both fine.
- Calculate: Press Calculate to convert the decimal to a fraction.
- Read the improper fraction: The large result is the reduced improper fraction, for example 7/4 for 1.75.
- Read the mixed number: When the absolute value is at least 1, the mixed-number form appears below, for example 1 and 3/4.
Formula and variables
Split the decimal into its whole part n and fractional part f. By place value, f equals its digits over a power of ten; simplifying gives p/q with no common factor. The improper fraction is (n × q + p)/q. This calculator obtains p/q through the continued-fraction expansion of f, whose convergents are always in lowest terms.
d = n + f = n + p/q, where p/q is the fractional part f in lowest terms- d — Decimal value
- The decimal number entered. (unitless)
- n — Whole part
- The integer part of the decimal (the digits left of the decimal point). (unitless)
- f — Fractional part
- The part of the decimal after the point, between 0 and 1. (unitless)
- p/q — Reduced fraction
- The fractional part written in lowest terms. (unitless)
Worked example: convert 1.75 to a fraction
Convert the decimal 1.75 into both an improper fraction and a mixed number.
- Decimal
- 1.75
- Separate the whole and fractional parts: 1.75 = 1 + 0.75.
- The last digit of 0.75 is in the hundredths place, so 0.75 = 75/100.
- Divide numerator and denominator by 25: 75/100 = 3/4.
- Combine with the whole part: 1 and 3/4 = (1 × 4 + 3)/4 = 7/4.
Result: 1.75 = 7/4 = 1 and 3/4
Seven quarters and one and three quarters are two names for the same value. Use the improper fraction for further algebra and the mixed number for measurements and recipes.
Understanding your results
Improper fraction
The improper fraction expresses the entire value as a single numerator over a denominator. It is reduced to lowest terms, so no further simplification is needed.
Mixed number
The mixed number separates the whole part from the fractional part and is shown only when the absolute value of the decimal is at least 1. For a decimal between -1 and 1, the improper fraction is already a proper fraction.
Integers
A decimal with no fractional part, such as 3 or 3.0, converts to itself over 1: 3/1. No mixed number is shown because there is no fractional remainder.
Assumptions
- The input is a finite decimal number; repeating notation such as 0.(3) is not parsed.
- The fraction is reported in lowest terms with a positive denominator.
- Negative decimals keep their sign on the numerator of the improper fraction and on the mixed number.
Limitations
- Repeating decimals must be rounded or entered with enough digits; for example, entering 0.3333333333333333 yields 1/3, while 0.3333 yields 3333/10000.
- Extremely large or small magnitudes are limited by standard double-precision floating-point representation.
- Fractions are exact for terminating decimals within floating-point precision; the calculator does not display measurement-style fractions with a fixed denominator such as sixteenths unless that is the exact reduced value.
Common mistakes
- Forgetting to reduce the fraction: 75/100 is correct but not simplified; the answer is 3/4.
- Writing the denominator from the wrong place value, for example treating 0.05 as 5/10 instead of 5/100.
- Dropping the sign when converting a negative decimal such as -0.5.
- Treating a rounded display of a repeating decimal (like 0.33) as the exact fraction 1/3.
- Mixing up the improper fraction and the mixed number, which are two forms of the same value.
Practical use cases
Homework and algebra
Convert decimals to exact fractions so equations can be solved without rounding error, and check manual place-value conversions.
Woodworking and machining
Turn a decimal measurement such as 0.375 inches into the familiar ruler fraction 3/8 inch.
Cooking and scaling
Express decimal quantities like 0.75 or 1.25 cups as 3/4 or 1 and 1/4 cups for measuring tools marked in fractions.
Planning and decision guide
Prefer the improper fraction for further calculation
Fraction arithmetic, ratios, and algebra are simpler with a single numerator and denominator. Convert back to a mixed number only for the final reported answer when the context calls for it. For arithmetic on the resulting fractions, use the fraction calculator.
Repeating decimals need exact treatment
A decimal with a bar over repeating digits is exact, but its typed approximation is not. Entering more repeating digits gets closer to the exact fraction; for the exact value, convert the repeating decimal algebraically (for example, x = 0.333... gives 10x − x = 3, so x = 1/3).
Match the denominator to the tool you are using
Rulers and wrenches come in powers of two (halves, quarters, eighths, sixteenths). A decimal such as 0.6875 is exactly 11/16, but 0.68 is 17/25 and must be approximated to the nearest sixteenth for a physical tool.
Frequently asked questions
How do I convert a decimal to a fraction by hand?
Write the digits after the decimal point over the place value of the last digit (tenths, hundredths, and so on), then simplify. For example, 0.75 = 75/100 = 3/4. If there is a whole part, keep it and attach the fraction to make a mixed number.
What is 0.75 as a fraction?
0.75 = 75/100, which reduces to 3/4.
What is the difference between an improper fraction and a mixed number?
They represent the same value. An improper fraction such as 7/4 keeps everything in one fraction, while a mixed number such as 1 and 3/4 separates the whole part from the fractional part.
Can this calculator convert repeating decimals?
Only approximately. Entering 0.3333333333333333 produces 1/3 because enough digits are supplied, but entering 0.3333 produces 3333/10000. For an exact repeating-decimal conversion, use algebra or a dedicated repeating-decimal tool.
Why is the fraction already in lowest terms?
The conversion uses the continued-fraction expansion of the fractional part. Its convergents always have no common factor between numerator and denominator, so the result is reduced by construction.
How do negative decimals convert?
The sign is preserved: -2.5 converts to -5/2, shown as the mixed number -2 and 1/2.
Sources and review
- Prealgebra 2e, Section 5.1: Decimals — Convert Decimals to Fractions or Mixed Numbers — OpenStax, Rice University. Accessed 2026-08-19.
- Continued Fraction — Wolfram MathWorld. Accessed 2026-08-19.
Reviewed 2026-08-19.