Long Division with Decimals Calculator
Divide numbers into decimal places with long division — move the decimal point, bring down zeros, and calculate to any place count (truncated, not rounded).
Dividing into decimals
When a division does not come out evenly, you can continue past the remainder into decimal places. If the divisor itself is a decimal, first shift both decimal points to make the divisor a whole number, then divide as usual and bring down zeros.
The steps
- Shift the decimal point in the divisor to make it whole, and shift the dividend the same amount.
- Place the decimal point in the quotient directly above its position in the dividend.
- Divide, and once the dividend runs out of digits, bring down zeros.
- Stop at the chosen number of places (truncate) or when the remainder becomes 0.
Worked example: 4.71 ÷ 3.2 to 3 places
Shift both points one place: 47.1 ÷ 32. Then divide and bring down zeros to get 1.471 (truncated at 3 places — the true value continues 1.4718...).
Terminating division: 31 ÷ 16
Bringing down zeros gives 1.9375 with a remainder of 0, so 31 ÷ 16 = 1.9375 exactly.
Repeating decimal: 22 ÷ 15
The remainder repeats, so the quotient repeats: to 3 places it is 1.466, and to 6 places 1.466666. Notice it is truncated, not rounded to 1.467.
Calculate to vs round to
- Calculate to n places — stop and drop the rest (1.466).
- Round to n places — adjust the last digit based on the next one (1.467).
This calculator truncates. For whole-number quotients with a remainder, use long division with remainders, and to round a result use rounding numbers.
Frequently asked questions
- How do you divide by a decimal?
- Move the decimal point in the divisor to the right until it becomes a whole number, and move the point in the dividend the same number of places. The quotient stays the same. For 4.71 divided by 3.2, shift both one place to get 47.1 divided by 32.
- Why move both decimal points the same amount?
- Multiplying the dividend and divisor by the same power of ten does not change the quotient — it is the same as multiplying a fraction top and bottom by the same number. It only makes the divisor a whole number so ordinary long division works.
- What does bringing down a zero do?
- Once you pass the decimal point in the dividend, you keep bringing down zeros to continue the division into tenths, hundredths, and beyond. Each zero brought down adds one more decimal place to the quotient.
- Does this calculator round the answer?
- No. It calculates to the number of places you choose and truncates — it simply stops. So 22 divided by 15 to three places is 1.466, not the rounded 1.467. Use a rounding calculator if you need rounding.
- What is a repeating decimal?
- When the remainder starts repeating, the quotient digits repeat forever, like 22 divided by 15 giving 1.4666.... Ask for more places to see the pattern, such as 1.466666 to six places.
- When does the division stop exactly?
- When a remainder of 0 appears, the division terminates and the quotient is exact — for example 31 divided by 16 is exactly 1.9375, and 3 divided by 8 is exactly 0.375.
- How many decimal places can I request?
- Between 1 and 20. The default is 3. More places reveal repeating patterns; fewer give a quick estimate.