Decimal long division calculator
4.5 ÷ 0.08 = 56.25 by decimal long division: move both decimal points two places to get 450 ÷ 8, then bring down two zeros past the decimal point.
Quotient
- Quotient Exact.
- 56.25
- Decimal point moved Moving both decimal points the same number of places multiplies both numbers by the same power of ten, so the quotient is unchanged.
- 2 places in both numbers: 450 ÷ 8
- Check The quotient times the divisor gives back the dividend.
- 56.25 × 0.08 = 4.5
| Step | Bring down | Working value | Quotient digit | Subtract 8 x digit | Remainder |
|---|---|---|---|---|---|
| 1 | 5 | 45 | 5 | 5 x 8 = 40 | 5 |
| 2 | 0 | 50 | 6 | 6 x 8 = 48 | 2 |
| 3 | 0, after the decimal point | 20 | 2 | 2 x 8 = 16 | 4 |
| 4 | 0, after the decimal point | 40 | 5 | 5 x 8 = 40 | 0 |
- The decimal point in the quotient sits directly above the decimal point in the shifted dividend. Past the dividend's last digit, each step brings down a 0.
How the Long Division Calculator works
Long division of decimals by decimals starts by making the divisor a whole number. Move its decimal point right until it is at the end, then move the dividend's decimal point the same number of places, adding zeros if the dividend runs out of digits. Both numbers are multiplied by the same power of ten, so the quotient does not change.
Worked example: 4.5 ÷ 0.08.
0.08 needs its decimal point moved two places to become 8. Moving 4.5 two places gives 450, with one zero added. The division is now 450 ÷ 8.
8 does not go into 4, so take 45: 8 goes in 5 times, 5 × 8 = 40, remainder 5. Bring down the 0 to make 50: 6 times, 6 × 8 = 48, remainder 2. The dividend has run out, so write a decimal point in the quotient and bring down a 0: 20 goes 2 times, 2 × 8 = 16, remainder 4. Bring down another 0: 40 goes 5 times exactly.
The quotient is 56.25. Its decimal point sits directly above the decimal point in the shifted dividend.
The division stops when the remainder is 0 or the quotient has as many decimal places as needed. 10 ÷ 3 never reaches 0: every step leaves a remainder of 1, so the 3 repeats and 10 ÷ 3 = 3.3333 to four places. To round, work one digit past the place you want: 2 ÷ 3 is 0.666..., which is 0.67 to two places.
A whole-number divisor needs no shift at all. 7.65 ÷ 3 is divided as it stands, with the decimal point carried straight up into the quotient, giving 2.55.
Long Division Calculator FAQ
Why can you move both decimal points?
Moving a decimal point one place right multiplies a number by 10. Doing it to both numbers multiplies the dividend and the divisor by the same amount, which leaves the quotient alone: 4.5 ÷ 0.08 = 450 ÷ 8.
What if the dividend has more decimal places than the divisor?
Move both points only as far as the divisor needs. 12.675 ÷ 0.5 becomes 126.75 ÷ 5, and the decimal point left in the dividend is carried up into the quotient: 25.35.
How many decimal places should I carry?
As many as the answer needs, plus one more to round with. Money needs two: $10 split 3 ways is 3.333..., which rounds to $3.33 each.