How to do long division when the divisor is a decimal?

To perform long division with a decimal divisor, the key is to transform the problem into one with a whole number divisor. Here's how to do it:

Steps for Long Division with Decimal Divisor

The process involves adjusting both the divisor and the dividend to eliminate the decimal in the divisor.

1. Identify the Divisor and Dividend: Determine which number is the divisor (the number you are dividing by) and which is the dividend (the number being divided).

2. Eliminate the Decimal in the Divisor:

   • Move the Decimal Point: Count how many places you need to move the decimal point to the right in the divisor to make it a whole number.
   • Adjust the Dividend: Move the decimal point in the dividend the same number of places to the right. Add zeros if necessary.

   Referencing the provided information: "If the decimal is in the divisor, the number you are dividing by, or both the divisor and the dividend, move the decimal point in the divisor over to the right to make it a whole number, and move the decimal in the dividend the same number of spaces to the right as the divisor."

3. Perform Long Division as Usual: Once the divisor is a whole number, perform the long division steps as you normally would.

4. Place the Decimal Point in the Quotient: The decimal point in the quotient (the answer) should be directly above the decimal point in the adjusted dividend.

Example

Let's say you want to divide 14.4 by 1.2:

1. Problem: 14.4 ÷ 1.2

2. Adjust Decimal:

   • Move the decimal one place to the right in 1.2, making it 12.
   • Move the decimal one place to the right in 14.4, making it 144.

3. New Problem: 144 ÷ 12

4. Long Division:

         12
   12|144
      12
      ---
       24
       24
       ---
        0

5. Answer: 14.4 ÷ 1.2 = 12

Table Summary

Step	Description	Example (14.4 ÷ 1.2)
1. Identify Divisor/Dividend	Determine which number is the divisor and which is the dividend.	Divisor: 1.2, Dividend: 14.4
2. Adjust Decimal	Move the decimal in the divisor to make it a whole number, and move the decimal the same amount in the dividend.	1. 2 becomes 12, 14.4 becomes 144
3. Perform Long Division	Divide as usual with the new whole number divisor.	144 ÷ 12 = 12
4. Place Decimal in Quotient	Align the decimal point in the quotient with that of the dividend.	N/A (In this case, moving the decimal made both whole numbers.)
Final Answer		12

By following these steps, you can confidently tackle long division problems involving decimal divisors.