Fraction to Decimal Calculator: Quick and Simple Conversion

Two directions, one page

The top section divides your numerator by your denominator to get a decimal, and specifically detects repeating decimals by tracking remainders during long division — when a remainder repeats, it marks that repeating block with an overline instead of just truncating the digits. The bottom section does the reverse, converting a typed decimal back into a fraction using a continued-fraction search.

Worked example: fraction to decimal

Enter 1 as the numerator and 3 as the denominator. Long division of 1 ÷ 3 never terminates: 10÷3 = 3 remainder 1, then 10÷3 = 3 remainder 1 again — the remainder 1 repeats immediately, so the calculator recognizes the whole decimal expansion as the repeating digit "3" and displays it as 0.3 with an overline (the same as writing 0.333...). The "standard decimal" line beneath it shows 0.3333333333 rounded to ten digits, for comparison.

Worked example: decimal to fraction

Enter 0.75. The tool's continued-fraction search converges on numerator 3, denominator 4 — 0.75 = 3/4 exactly, and it displays "Decimal value: 0.7500000000" to confirm the round-trip matches your input.

Why some fractions repeat and others don't

A fraction terminates in decimal form only if its denominator (in lowest terms) has no prime factors other than 2 and 5 — the prime factors of 10. 3/4 terminates (4 = 2²) but 1/3 does not, because 3 isn't a factor of any power of 10.

Constraints

A zero denominator is rejected outright. The repeating-decimal detector only searches within the digits it computes (up to where a remainder repeats), so it won't misidentify a coincidental digit pattern as repeating.