Continued fraction explorer
See the exact convergents of a fraction or decimal, and compare the error at each step.
Enter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −120 to 120. Choose 1 to 256 convergents. Decimal input is an exact finite rational, not a symbolic irrational constant. Decimal previews truncate after 12 places; exact fractions and signed errors are preserved. A term-limit stop is explicitly distinguished from a terminated expansion. Enter a decimal, scientific notation or integer fraction, such as 355/113. Results update as you type. Up to 300 characters.
Your result
How to use Continued fraction explorer
- Enter the exact number you want to approximate.
- Set the maximum number of convergents.
- Compare the coefficients, rational approximations and exact errors; download the full table.
Useful next steps
How to use it
See the exact convergents of a fraction or decimal, and compare the error at each step.
Limits and assumptions
Enter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −120 to 120. Choose 1 to 256 convergents. Decimal input is an exact finite rational, not a symbolic irrational constant. Decimal previews truncate after 12 places; exact fractions and signed errors are preserved. A term-limit stop is explicitly distinguished from a terminated expansion.
Keep the exact values
Download JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.