A decimal is another place-value form of a rational number: positions to the right of the point represent tenths, hundredths, and smaller powers of ten.
Use it to rewrite the same quantity in a form suited to estimation, comparison, or calculation.
A displayed finite decimal can be an approximation; repeating expansions need their repeating pattern preserved.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Understand the subject
How are fractions and decimals connected?
A fraction and a decimal can name the same rational number. Division expands a fraction into decimal place values; place value turns a finite decimal back into a fraction.
Use conversion to compare formats, enter exact values, or communicate a quantity in the notation best suited to the task.
The relationship
The defining equation
a/b = a ÷ b
A finite decimal uses a denominator that is a power of ten before reduction.
See the structure
One value, two notations
3/8=0.375
Worked example
Convert 0.375 to a fraction
0.375 = 375/1000 = 3/8
Interpret with care
What the result does—and does not—mean
Some rational numbers repeat forever in decimal notation. A rounded decimal is an approximation, not necessarily the original exact fraction.
Quick guide
How to use this calculator
Enter values using the notation shown beside each field.
Choose a calculation mode when the tool offers more than one interpretation.
Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
decimal = numerator/denominator
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
0.375 = 3/8.
decimal = numerator/denominator
Supported inputs
Precision and limits
Finite, bounded input
Integers, finite decimals, fractions, and mixed numbers are evaluated with exact rational arithmetic wherever the operation permits.
Notation
Enter fractions as a/b and mixed numbers as w n/d. A denominator can never be zero.
