The method in 3 steps
In 12.6 ÷ 0.3 = 42, 12.6 is the dividend (the number being divided), 0.3 is the divisor (the number you divide by), and 42 is the quotient (the answer).
- Make the divisor a whole number. Work out how many places its decimal point needs to move to the right.
- Move the dividend's decimal point the same number of places. This multiplies both numbers by the same factor: 10, 100, and so on.
- Use long division on the new calculation. The dividend is allowed to remain a decimal.
Multiplying both numbers by the same factor leaves the answer unchanged. When the divisor is already a whole number, no decimal-point move is needed.
Example 1: 12.6 ÷ 0.3
1. Start with the original calculation
12.6 ÷ 0.3
The divisor is 0.3.
2. Multiply both numbers by 10
12.6 × 10 = 126
0.3 × 10 = 3
Move both decimal points one place to the right.
3. Divide the whole numbers
126 ÷ 3 = 42
Check with the original divisor: 42 × 0.3 = 12.6.
Example 2: A decimal answer, 3.75 ÷ 1.5
Multiply both numbers by 10 to make 1.5 a whole number:
3.75 ÷ 1.5 = 37.5 ÷ 15 = 2.5
Keep the decimal point in 37.5. In the layout shown here, write the answer's decimal point directly above the decimal point in the transformed dividend, 37.5.
- 15 goes into 37 twice. Write 2 in the ones place of the answer. Multiply 15 × 2 = 30, then subtract: 37 − 30 = 7.
- Write the decimal point after the 2, directly above the decimal point in 37.5.
- Bring down the next digit, 5, to work with 75. Since 15 × 5 = 75, write 5 in the tenths place of the answer.
- Subtract to get 0. The division is finished, and the answer is 2.5.
Check: 2.5 × 1.5 = 3.75. There is no final decimal-point move to undo: the transformed calculation has the same answer as the original problem.
When to add zeros
When you need more places for the decimal-point move
For 3.5 ÷ 0.05, move both decimal points two places to the right. Writing 3.5 = 3.50 does not change the value:
3.50 × 100 = 350
0.05 × 100 = 5
3.5 ÷ 0.05 = 350 ÷ 5 = 70
When you run out of digits during long division
For 1 ÷ 4, write 1 = 1.00 to continue. 4 goes into 1 zero times, so start the answer with 0. Bring down a zero to work with 10: 4 goes into 10 twice, leaving 2. Bring down another zero to work with 20: 4 goes into 20 five times, leaving 0.
1 ÷ 4 = 0.25
1 equals 1.00, not 10. To keep the value unchanged, add zeros at the end of the fractional part, after the decimal point. Bringing down a digit moves to the next place value; it does not multiply the original problem by 10.
What if the divisor is already a whole number?
For 4.8 ÷ 3 = 1.6, use long division without moving either decimal point first.
Mistakes to avoid
Wrong: Change only the divisor
12.6 ÷ 3 = 4.2
4.2 ≠ 42
This changes the original problem, 12.6 ÷ 0.3, instead of making it easier to calculate.
Correct: Multiply both by 10
12.6 ÷ 0.3 = 126 ÷ 3 = 42
The quotient stays the same.
- Do not remove both decimal points independently: 3.75 ÷ 1.5 becomes 37.5 ÷ 15, not 375 ÷ 15.
- Do not move the answer's decimal point again at the end. The answer 2.5 is already correct.
Check your understanding
Which calculation has the same answer as 6.3 ÷ 0.3?
- A: 6.3 ÷ 3
- B: 63 ÷ 3
Show the answer and why
B. Multiplying 0.3 by 10 gives 3, so multiply 6.3 by 10 as well to get 63. 63 ÷ 3 = 21. Check with the original divisor: 21 × 0.3 = 6.3.
Explore the written steps in the calculator
Open the same examples to explore the transformation and long-division steps.
Where to go next
- Decimal Long DivisionOpen the full calculator when you want the move, the transformed equation, and the written steps together.
- Long Division CalculatorCompare this method with whole-number long division when no decimal-point move is needed.
- Decimal Long MultiplicationStay with decimals and compare moving the point before dividing with putting it back after multiplying.
Frequently asked questions
Why can I multiply both numbers by 10 or 100?
Multiplying the dividend and divisor by the same factor leaves the quotient unchanged. Both 12.6 ÷ 0.3 and 126 ÷ 3 have the answer 42.
Must both numbers become whole numbers?
No. Make the divisor a whole number first. In 3.75 ÷ 1.5, the new calculation is 37.5 ÷ 15, and it is fine for 37.5 to remain a decimal.
Where does the answer's decimal point go?
In the layout used on this page, place it directly above the decimal point in the transformed dividend. For 3.75 ÷ 1.5, use the position in 37.5 ÷ 15, not the original 3.75.
Does dividing by 0.30 need a two-place move?
0.30 and 0.3 have the same value, so one place is enough to make the divisor a whole number. Multiplying both numbers by 100 also works, but multiplying both by 10 keeps the calculation smaller.
Can I divide by zero?
No. The divisor cannot be zero. The dividend can be zero: for example, 0 ÷ 0.3 = 0.
Will adding zeros always make the division finish?
No. Some answers keep repeating, such as 1 ÷ 3 = 0.333…. A finite value such as 0.33 is only an approximation, so write 1 ÷ 3 ≈ 0.33.
See also
- Study & classroomWorksheets, graph paper, and classroom helpers.
- Math & statisticsBrowse the wider math collection.
- All topicsReturn to the main topics directory.