Long division with decimals may seem like a daunting task, but with some practice and patience, it can become a breeze. Whether you’re a student learning long division for the first time or an adult refreshing your math skills, this guide will walk you through the steps of long division with decimals.
Step 1: Set up the Problem
The first step in long division with decimals is to set up the problem. Write the dividend (the number being divided) and the divisor (the number you are dividing by) as you normally would, with the divisor outside the long division bracket and the dividend inside.
For example, if you are dividing 4.56 by 0.12, your setup would look like this:
| 0.12 | | 4.56 |
Step 2: Move the Decimal Point
Next, move the decimal point in the dividend to the right as many places as necessary to make it a whole number. Keep track of how many places you move the decimal point and move it the same number of places in the divisor.
For example, in our problem of 4.56 ÷ 0.12, we would move the decimal point in 4.56 two places to the right to make it 456. We would also move the decimal point in 0.12 two places to the right to make it 12.
| 0.12 | | 4.56 |
| --> | |
| 12 | | 456 |
Step 3: Divide and Write the Quotient
Divide the new dividend (the number you moved the decimal point in step 2) by the divisor. Write the quotient above the long division bracket.
For our example of 456 ÷ 12, the quotient is 38.
| 0.12 | | 4.56 |
| --> | |
| 12 | | 456 |
| 38 | | |
Step 4: Multiply and Subtract
Multiply the divisor by the quotient and write the result below the new dividend. Subtract the result from the new dividend to get the remainder.
For our example of 456 ÷ 12 with a quotient of 38, we would multiply 12 by 38 to get 456, then subtract 456 from 456 to get a remainder of 0.
| 0.12 | | 4.56 |
| --> | |
| 12 | | 456 |
| 38 | | 456 |
| -- | |
| 0 | |
Step 5: Add the Decimal Point and Bring Down the Next Digit
If there are more digits in the dividend, add a decimal point to the remainder and bring down the next digit. If there are no more digits in the dividend, you have your answer.
For our example of 4.56 ÷ 0.12, we have a remainder of 0, so our answer is 38.
| 0.12 | | 4.56 |
| --> | |
| 12 | | 456 |
| 38 | | 456 |
| -- | |
| 0 | |
| 38 | |
Congratulations, you now know how to do long division with decimals!
Tips and Tricks
Here are a few tips and tricks to help you become a long division master:
- Make sure you move the decimal point in both the dividend and divisor the same number of places.
- Check your work by multiplying your quotient by your divisor and adding the remainder. The result should be equal to the dividend.
- If you have a repeating decimal in your dividend, you can convert it to a fraction and then divide normally.
- Practice, practice, practice! The more you do long division with decimals, the easier it will become.
Conclusion
Long division with decimals may take some time to master, but with practice and patience, you can become a pro. Remember to set up the problem, move the decimal point, divide and write the quotient, multiply and subtract, and add the decimal point and bring down the next digit. Follow these steps and you’ll be dividing decimals like a champ in no time!