Long Division Calculator with Decimals

Perform long division with decimal numbers step by step. Calculate quotient to any decimal place precision.

Perform long division with step-by-step work. Supports decimals and shows quotient with remainder.

Divisor
Dividend
Decimal places:
=
?
Max 15 characters per number
Try:
help_outlineHow to Useexpand_more

Dividing Decimal Numbers

This calculator performs long division with positive or negative decimal numbers. Enter the dividend and divisor, choose how many decimal places you want in your answer, and see each step of the calculation process.

How to Do Long Division with Decimals:

  1. Handle decimal divisors: If the divisor has a decimal, move it all the way right. Move the dividend's decimal the same number of places.
  2. Position the decimal: Place a decimal point in the quotient directly above the decimal in the dividend.
  3. Divide step by step: Divide, multiply, subtract, bring down - repeat the process.
  4. Continue to desired precision: Keep dividing until the remainder is zero or you reach your desired decimal places.
  5. Check for repeating decimals: If the remainder starts repeating, your answer is a repeating decimal.

Parts of Division:

  • Dividend: The number being divided (inside the division bracket)
  • Divisor: The number you divide by (outside the bracket)
  • Quotient: The answer to the division problem
  • Remainder: What's left over after division
infoWhat is Long Division Calculator with Decimals?expand_more

Long division is a standard algorithm for dividing large numbers by breaking the problem into a series of smaller, manageable steps. It works by repeatedly dividing, multiplying, subtracting, and bringing down digits until the problem is solved.

When working with decimal numbers, the key is to first eliminate any decimal in the divisor by moving decimal points. The quotient's decimal is then placed directly above the dividend's decimal point. This ensures place values remain aligned.

Note on decimal places vs. rounding: Calculating to 3 decimal places means stopping at the third decimal digit (e.g., 22 / 15 = 1.466). Rounding to 3 decimal places requires calculating the fourth digit first to determine rounding (1.467).

functionsFormulaexpand_more

Division Relationship:

Dividend = Divisor x Quotient + Remainder

This relationship can verify your answer is correct.

Long Division Steps:

1. Divide: How many times does divisor go into current portion?

2. Multiply: Multiply quotient digit by divisor

3. Subtract: Subtract product from current portion

4. Bring down: Bring down next digit from dividend

5. Repeat: Continue until no more digits or desired precision

Decimal Divisor Handling:

Move decimal right in divisor until it's a whole number

Move decimal the same places in dividend

Example: 4.71 / 3.2 becomes 47.1 / 32

lightbulbExamplesexpand_more

Example 1: 471 / 32 (to 3 decimal places)

4 / 32 = 0 remainder 4

47 / 32 = 1 remainder 15

151 / 32 = 4 remainder 23, then 230 / 32 = 7 remainder 6...

Quotient = 14.718

Example 2: 31 / 16 (to 6 decimal places)

31 / 16 = 1 remainder 15

Continue: 150 / 16 = 9, 60 / 16 = 3, 120 / 16 = 7, 80 / 16 = 5...

Quotient = 1.937500 (exact, terminates)

Example 3: 22 / 15 (repeating decimal)

22 / 15 = 1 remainder 7

70 / 15 = 4 remainder 10

100 / 15 = 6 remainder 10 (repeats!)

Quotient = 1.466666... (repeating 6)

Example 4: 4.71 / 3.2 (decimal divisor)

First: Move decimals to get 47.1 / 32

47 / 32 = 1 remainder 15

151 / 32 = 4 remainder 23...

Quotient = 1.471...

quizFAQexpand_more
How do I handle a decimal in the divisor?expand_more
Move the decimal point in the divisor all the way to the right to make it a whole number. Count how many places you moved it, then move the decimal in the dividend the same number of places to the right. Add zeros to the dividend if needed. For example, 4.71 / 3.2 becomes 47.1 / 32.
What's the difference between calculating to 3 decimal places and rounding to 3 decimal places?expand_more
Calculating to 3 decimal places means you stop the division once you reach the third decimal digit. Rounding to 3 decimal places requires calculating at least the fourth decimal digit to determine whether to round up or down. For 22/15: calculated to 3 places = 1.466, but rounded to 3 places = 1.467.
How do I know if my answer is a repeating decimal?expand_more
If you notice the remainder starts repeating the same values you've seen before, your answer is a repeating decimal. For example, when dividing 22 by 15, the remainder 10 keeps appearing, producing the repeating digit 6 (1.4666...).
What's the difference between quotient and remainder?expand_more
The quotient is the result of division - how many times the divisor fits into the dividend. The remainder is what's left over after the division. For 17 / 5: the quotient is 3 (5 goes into 17 three times), and the remainder is 2 (17 - 15 = 2).
How can I verify my long division answer?expand_more
Use the division relationship: Dividend = Divisor x Quotient + Remainder. Multiply your quotient by the divisor and add the remainder. If you get back to the original dividend, your answer is correct. For 17 / 5 = 3 R2: check 5 x 3 + 2 = 17.