Dividing with decimals works exactly like whole-number long division with two extra rules: first make the divisor a whole number, and then keep bringing down zeros after the decimal point for as many places as you need. This calculator does both, draws the layout, tells you whether the decimal terminates or repeats, and rounds the result to your chosen number of places.
How to use the calculator
- Enter the dividend and the divisor. Either can be a decimal or negative.
- Choose how many decimal places to carry, from 0 to 20.
- The tape shows the rounded quotient, the exact quotient with any repeating block marked by a bar, the same value in parenthesis notation, and the exact fraction.
- The layout shows the shifted problem with gray zeros brought down after the point.
The method
- Make the divisor whole. Count its decimal places and move both decimal points that many places to the right. Add zeros to the dividend if it runs out of digits.
- Divide as usual, writing each quotient digit above the digit you brought down.
- Place the decimal point in the quotient directly above the point in the dividend.
- Bring down zeros after the last digit of the dividend and keep dividing until the remainder is 0, a remainder repeats, or you have one more digit than you need for rounding.
Worked example: 15.4 ÷ 0.6
- The divisor 0.6 has one decimal place, so multiply both numbers by 10: 154 ÷ 6.
- 6 goes into 15 twice: 15 − 12 = 3. Bring down 4 → 34.
- 6 goes into 34 five times: 34 − 30 = 4. The whole-number digits are used up, so write the decimal point: 25.
- Bring down a 0 → 40. 6 goes in 6 times: 40 − 36 = 4. Bring down a 0 → 40 again.
- The remainder 4 repeats, so the 6 repeats forever: 25.666…, written 25.6̅ or 25.(6).
- Rounded to four places, the next digit is 6, so round up: 25.6667. As a fraction the exact answer is 77/3.
Terminating or repeating?
A quotient terminates only if, after the division is written as a fraction in lowest terms, the denominator has no prime factors other than 2 and 5. Otherwise the digits repeat.
| Division | Fraction | Decimal |
|---|---|---|
| 2.5 ÷ 4 | 5/8 | 0.625 (terminates) |
| 1 ÷ 3 | 1/3 | 0.333… (repeats “3”) |
| 22 ÷ 7 | 22/7 | 3.142857142857… (repeats “142857”) |
| 0.0015 ÷ 0.006 | 1/4 | 0.25 (terminates) |
The repeating block can never be longer than the divisor minus one, because there are only that many possible nonzero remainders. That is why 1 ÷ 7 repeats after six digits.
Common mistakes
- Moving only one decimal point. Shifting the divisor without shifting the dividend changes the answer by a power of 10.
- Forgetting zeros in the quotient. In 0.0015 ÷ 0.006 → 1.5 ÷ 6, the first quotient digit above the 1 is 0, so the answer starts 0.2…
- Rounding too early. Carry one extra digit and round once at the end. For general rounding rules see the rounding calculator, and to turn a repeating answer back into a fraction use the decimal to fraction calculator.
Frequently asked questions
How do you divide by a decimal?
Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. The answer does not change because you multiplied both numbers by the same power of 10. For 15.4 ÷ 0.6, move one place to get 154 ÷ 6.
Where does the decimal point go in the quotient?
Directly above the decimal point in the dividend, after you have made the divisor a whole number. Every digit you bring down after that point adds one decimal place to the answer.
How do I know if a decimal repeats?
Watch the remainders. If a remainder you have already seen appears again, the digits that follow will repeat forever. In 154 ÷ 6 the remainder 4 keeps coming back, so the 6 repeats: 25.666…
How is the answer rounded?
The calculator finds the digit after the last place you asked for. If it is 5 or more, the last kept digit goes up by one; otherwise it stays. 25.66666… to four places is 25.6667.