Long Division Calculator with Decimals

Divide any two numbers step by step with our free long division calculator. Handles decimals, remainders, and repeating decimals with a full worked solution. 

Parts of a Long Division Problem 

When you divide large numbers using long division, you get the answer through a step-by-step process. Our long division calculator works with four main parts: 

• Dividend: The number being divided, written inside the division bracket. For example, if you’re dividing 655, the dividend is 655.
• Divisor: The number you divide by, written outside the division bracket. For example, if you’re dividing by 5, the divisor is 5. 
• Quotient: The result of the division, written above the bracket. 
• Remainder: The value left over after division that can no longer be evenly divided. 

Our calculator lets you see the exact remainder by selecting ‘0 (Remainder),’ or a decimal answer rounded to a fixed number of decimal places.

How to Use This Calculator 

1. Divisor box: In the first box, enter your divisor, the number you are dividing by. 
2. Dividend box: In the second box, enter your dividend, the number you want to divide. 
3. In the dropdown menu, select how many decimal places you want in the answer. If you want the exact remainder instead of a decimal answer, select the ‘0 (Remainder)’ option. 

Long Division Formula 

The long division method uses this formula: 

Dividend = Divisor × Quotient + Remainder 

This formula always follows one strict rule: 0 ≤ Remainder < Divisor. 

How the Calculator Solves Long Division (Step by Step)

Our calculator repeats a simple four-step loop until the division is complete. This is commonly known as the Divide-Multiply-Subtract-Bring Down process.

1. Divide: See how many times the divisor fits completely into the first digit(s) of the dividend. Write that number as the next digit of the quotient. 

2. Multiply: Multiply the quotient digit you just wrote by the divisor, and write the result below the corresponding part of the dividend.

3. Subtract: Subtract this product from the number above it. What’s left is the remainder for this step.

4. Bring Down: Bring down the next digit of the dividend and write it beside the remainder. Repeat the process from step 1.

Example:

   Step-by-Step: 7.50 ÷ 6

   [D]ivide ➔ [M]ultiply ➔ [S]ubtract ➔ [B]ring Down

             1 . 2  5      <-- (Quotient)
           ___________
(Divisor) 6 | 7 . 5  0      <-- (Dividend)

            - 6  ↓  ↓       [D] 7 ÷ 6 = 1
            ---  ↓  ↓       [M] 1 × 6 = 6
              1  5  ↓       [S] 7 - 6 = 1, then [B]ring down 5

            - 1  2  ↓       [D] 15 ÷ 6 = 2
            ------- ↓       [M] 2 × 6 = 12
                 3  0       [S] 15 - 12 = 3, then [B]ring down 0

               - 3  0       [D] 30 ÷ 6 = 5
               -------      [M] 5 × 6 = 30
                    0       [S] 30 - 30 = 0  <-- (Final Remainder)

How the Calculator Handles Decimal Numbers 

If your divisor is a decimal number, like 1.5 or 0.25, dividing directly is difficult. That’s why our calculator automatically adjusts the numbers to make the division easier:

• Decimal Shift Rule: To turn a decimal divisor into a whole number, shift its decimal point to the right.
• You must shift the decimal point of the dividend to the right by the same number of places.
• For example, to divide 5.62 by 0.2, shift the divisor’s decimal point one place to the right, turning 0.2 into 2. To keep the division balanced, shift the dividend’s decimal point the same one place, turning 5.62 into 56.2. 56.2 ÷ 2 is now a whole-number problem, and it gives the exact same answer as 5.62 ÷ 0.2 = 28.1. 

Repeating Decimals 

Sometimes division does not end and the same remainder starts to repeat in a loop. In these cases, the decimal digits repeat infinitely – for example, 10 ÷ 3 = 3.3333… Our calculator detects this type of situation and shows the repeating decimal message.

Tested Examples

We tested the calculator with the following inputs to confirm it produces accurate results: 

Test Case 1 (Exact Remainder):

• Input: (Dividend) = 845, (Divisor) = 14, Decimal Places = 0 (Remainder)
• Output: (Quotient) = 60, (Remainder) = 5. (Answer: = 60 R 5).

Test Case 2 (Division of Decimal Number):

• Input: (Dividend) = 27.85, (Divisor) = 2.5, Decimal Places = 3
• Output: Quotient = 11.140. The calculator auto-adjusts and shows it solved the problem as 278.5 ÷ 25. 

Test Case 3 (Detect Repeating Decimal):

• Input: (Dividend) = 17, (Divisor) = 6, Decimal Places = 4
• Output: (Quotient) = 2.8333.

Common Long Division Mistakes to Avoid 

• Missing Zero: If, after bringing down a digit, the number is still smaller than the divisor, you must write a zero in the quotient. Many people forget this step and get the wrong answer.
• Wrong Decimal Shifting: When you shift the divisor’s decimal point (by multiplying it by 10, 100, etc.) to make it a whole number, you must shift the dividend’s decimal point by the same amount.
• Remainder Check: After every subtraction step, the remaining value should always be smaller than the divisor. If it’s equal to or greater than the divisor, the quotient digit you wrote was too small.

References

• Khan Academy, Long Division with Decimals: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-dividing-decimals/v/long-division-with-decimals
• Math Is Fun, Long Division (intro): https://www.mathsisfun.com/long_division.html
• Math Is Fun, Long Division to Decimal Places: https://www.mathsisfun.com/long_division3.html
• Math Is Fun, Long Division With Remainders: https://www.mathsisfun.com/long_division2.html
• Wolfram MathWorld, Long Division: https://mathworld.wolfram.com/LongDivision.html
• Wikipedia, Long Division : https://en.wikipedia.org/wiki/Long_division

Disclaimer 

This calculator is intended for educational and reference purposes only. For critical financial or scientific work, please double-check the results independently.

Published date: February 2026, Last verified: September 2026