Dividing by a decimal number may seem difficult at first. After all, you never learned the "0.7 table." The secret is to change the division problem to a format that only uses whole numbers. Once you have rewritten the problem in this way, it will become a regular long division problem.
Steps
Part 1 of 2: Write the Problem as an Ordinary Division Problem
Step 1. Write your division problem
Use a pencil in case you want to check your calculations.
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Example:
How much is it 3 ÷ 1, 2?
Step 2. Write the whole number as a decimal
Write a decimal point after the whole number and then write zeros after the decimal point. Do this until the two numbers have the same number of places to the right of the decimal point. This will not change the value of the whole number.
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Example:
In the problem 3 ÷ 1, 2, the whole number is 3. Since 1, 2 has a place to the right of the decimal point, you will have to rewrite 3 as 3, 0, so that it also has a place after the decimal point. Now, the problem will be as follows: 3, 0 ÷ 1, 2.
- Warning: do not add leading zeros to the decimal point. The number 3 is the same as 3, 0, or 3, 00, but it is not the same as 30 or 300.
Step 3. Move the decimal points to the right until you have whole numbers
In division problems, you are allowed to move decimal points, but only if you move them the same number of places for each number. This allows you to convert the problem to whole numbers.
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Example:
To convert 3, 0 ÷ 1, 2 to whole numbers, you will have to move the decimal points one space to the right. In this way, 3, 0 will become 30 and 1, 2 will become 12. Now, the problem will be as follows: 30 ÷ 12.
Step 4. Write the problem as a long division
Put the dividend (usually the largest number) under the long division symbol. Write the divisor outside. Now you will have a common long division problem that uses whole numbers. If you want to remember how to do a long division, check out the next section.
Part 2 of 2: Solve the Long Division Problem
Step 1. Find the first digit of the answer
Begin to solve the problem as you normally would, comparing the divisor with the first digit of the dividend. Find the number of times the divisor contains this digit, and then write this number on top of that digit.
- Example: you want to divide 12 by 30. Compare 12 with the first digit of the divisor: 3. Since 12 is greater than 3, then it will be contained in the latter 0 times. Writes 0 above 3, on the answer line.
Step 2. Multiply this digit by the divisor
Write the product (the result of the multiplication) below the dividend. Write it directly below the first digit of the dividend, since this is the digit you just worked with.
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Example:
Since 0 x 12 = 0, write 0 below 3.
Step 3. Subtract to find the difference
Subtract the product you just got from the digit above it. Write the answer below, on a new line.
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Example:
3 - 0 = 3, so you will have to write
Step 3. directly below 0.
Step 4. Move down the next digit
Lower the next digit of the dividend next to the number you just wrote.
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Example:
In this case, the dividend is 30. We already worked with the 3, so the next digit to lower is 0. Lower it next to your 3 to form
Step 30..
Step 5. Try to calculate how many times the divisor is contained in the new number
Then repeat the first step of this section to find the second digit of your answer. This time, compare the divisor with the number you just wrote on the bottom line.
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Example:
How many times is 12 in 30 contained? The closest number is 2, since 12 x 2 = 24. Write
Step 2. in the second space of the answer line.
- If you are not sure of the answer, do some multiplication until you find the answer that is closest to you. For example, if you think the answer is 3, multiply 12 x 3 and you will get 36. This number is too large, since the idea is to calculate how many times it is contained in 30. Try the smallest and immediate number, 12 x 2 = 24. This does match, so 2 is the correct answer.
Step 6. Repeat the steps above to calculate the next number
This is the same long division process you just used that should be used in any long division problem:
- Multiply the new digit on the answer line by the divisor: 2 x 12 = 24.
- Write the product on a new line, below your dividend: Write 24 directly below 30.
- Subtract the line below the one above: 30 - 24 = 6; then write 6 below, on a new line.
Step 7. Continue until you reach the end of the answer line
If there is still another digit missing from the dividend, lower it and solve the problem in the same way. If you have already reached the end of the answer line, go to the next step.
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Example:
you just wrote
Step 2. at the end of the answer line. Go to the next step.
Step 8. Add a decimal to extend the dividend, if necessary
If the division was exact, you will get "0" as the result of the last subtraction. This means that you are done, and the answer to your problem will be a whole number. But if you have already reached the end of the answer line and there is still something left to divide, you will have to extend the dividend by adding a decimal point followed by a 0. Remember that this does not change the value of the number.
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Example:
You are already at the end of the answer line, but the result of the last subtraction is "6". Extend the "30" below the long division symbol by adding a ", 0" at the end. Write a decimal point in the same place on the answer line, but don't write anything afterwards.
Step 9. Repeat the same steps to find the next digit
The only difference here is that you have to move the decimal point up to the same place on the answer line. Once you have done this, you will have to find the other digits of the answer in the same way.
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Example:
move the new 0 down to the last line to form "60." Since 12 is contained in 60 exactly 5 times, you must write
Step 5. as the last digit on the answer line. Do not forget that you must put a decimal in the answer line, so that the final answer of the problem will be 2, 5.
Advice
- If the long division goes on for a long time, you can stop at any time and round to a close number. For example, to solve 17 ÷ 4, 20, simply calculate until you get to 4,047 and round your answer to "4, 05."
- Another option is to write it as a remainder (so the answer for 3 ÷ 1, 2 would be "2 with a remainder of 6"). However, since you're working with decimals right now, your teacher will probably expect you to solve the decimal part of the answer as well.
- If you follow the long division method correctly, you will always end up with the decimal point in the correct position or no decimal at all if the division is exact. Don't try to guess where to put the decimal point; it will often be a different place than the original numbers you started with.
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Remember the terms of a division:
- The dividend is the number that you are going to divide.
- The divisor is the number by which you are going to divide another number.
- The quotient is the answer to the problem.
- Putting them all together you get: Dividend ÷ Divisor = Quotient.