4/3 as a Decimal

4/3 as a decimal is 1.333…, with the 3 repeating forever. Unlike fractions with a denominator of 8 or 4, dividing by 3 never lands on a clean, finite answer - so this one is genuinely different from the eighths and quarters conversions on this site.

Why 4/3 Never Terminates

Dividing 4 by 3 with long division: 4 ÷ 3 = 1, remainder 1. Bring down a zero: 10 ÷ 3 = 3, remainder 1 again. Bring down another zero: 10 ÷ 3 = 3, remainder 1 - again. The remainder never reaches zero, so the digit 3 just keeps repeating. A fraction only terminates when its denominator (in lowest terms) is made up entirely of 2s and/or 5s - 3 is neither, so 4/3 repeats instead.

Writing a Repeating Decimal

Rather than writing an endless string of 3s, repeating decimals are usually shown with a bar over the part that repeats: 1.3̄ means "1.3333… forever." For everyday use, it's normal to round instead - 1.33 to two decimal places, or 1.333 to three - just keep in mind that's an approximation, not the exact value.

4/3 as a Mixed Number and a Percentage

Since 4 is larger than 3, 4/3 is an improper fraction - as a mixed number, it's 1 1/3 (one whole plus a remaining 1/3). As a percentage, multiplying the repeating decimal by 100 gives 133.333…%, usually written as approximately 133.3%. You can see this approximation yourself with the Percentage Calculator's “what percent is X of Y” mode - entering 4 as the part and 3 as the whole returns a rounded decimal, not the exact repeating value, since no calculator display can show infinitely many digits.