Long Division Calculator

Divide decimals exactly by long division: quotient to up to 20 places, repeating-decimal notation, integer quotient and remainder, and bring-down steps.

Interactive calculator · Method LONG-DIVISION-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

Both numbers are scaled by powers of 10 to whole numbers P and Q with the same ratio.

Your inputs

Try an example

Dividend (up to 15 significant digits) (number)

Divisor (up to 15 significant digits, not 0) (number)

Decimal places to compute (places)

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Quotient digits (truncated) 3.1428571428

Rounded quotient 3.1428571429

Exact decimal form 3.(142857)

Repeating block 142857 (6 digits, from decimal place 1)

Integer quotient and remainder 3 R 1

22 ÷ 7 = 22 ÷ 7 as whole numbers = 3 remainder 1; continuing the division gives 3.(142857).

How to use the calculator

Enter the dividend and divisor as decimals (a minus sign is allowed) and choose how many decimal places to compute.

What the result means

22 ÷ 7 is 3 remainder 1; continuing gives 3.1428571428… where the block 142857 repeats forever, so to 10 places it rounds to 3.1428571429.

Formula and units

Both numbers are scaled by powers of 10 to whole numbers P and Q with the same ratio. The integer quotient is P ÷ Q rounded toward zero, and the remainder = dividend − integer quotient × divisor (it keeps the dividend’s sign). Each further decimal digit = (10 × remainder) ÷ Q. A repeating decimal is detected when a remainder recurs; the digits between the two occurrences repeat forever and are shown in parentheses, e.g. 22 ÷ 7 = 3.(142857).

Worked examples

22 ÷ 7 to 10 places: Dividend (up to 15 significant digits): 22 number; Divisor (up to 15 significant digits, not 0): 7 number; Decimal places to compute: 10 places.
Example result: Quotient digits (truncated): 3.1428571428; Rounded quotient: 3.1428571429; Exact decimal form: 3.(142857); Repeating block: 142857 (6 digits, from decimal place 1); Integer quotient and remainder: 3 R 1.

7.5 ÷ 0.12 to 4 places: Dividend (up to 15 significant digits): 7.5 number; Divisor (up to 15 significant digits, not 0): 0.12 number; Decimal places to compute: 4 places.
Example result: Quotient digits (truncated): 62.5000; Rounded quotient: 62.5000; Exact decimal form: 62.5; Repeating block: none (terminates after 1 decimal place); Integer quotient and remainder: 62 R 0.06.

Limitations and common mistakes

Exact decimal arithmetic for plain decimal inputs up to 15 significant digits; exponents, fractions and thousands separators other than commas are not read. The truncated quotient drops later digits; the rounded quotient rounds half away from zero. Repeating blocks longer than 2,000 digits are reported but not shown.

Moving the decimal point in the divisor without moving it the same number of places in the dividend.

Sources and assumptions

Method LONG-DIVISION-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.