How do you divide a double number?

Dividing a double number involves applying the standard division process to a number that might have a decimal component, and by a divisor which could also have a decimal component. The core principle remains the same as whole number division: we determine how many times the divisor "fits into" the dividend. Here's how to break it down:

Understanding the Process

The process is based on the principle that we fit the divisor into each part of the dividend, then subtract and bring down the next digit, a method that aligns with the reference provided. The procedure involves several key steps:

• Setup: Write the dividend inside the division symbol and the divisor to the left of the symbol.
• Initial Division: Look at the first part of the dividend. Determine how many times the divisor fits into this part. Write this number above the dividend, in the quotient.
• Multiply and Subtract: Multiply the number you just wrote in the quotient by the divisor. Write the result under the part of the dividend you were working with and subtract the values.
• Bring Down: Bring down the next digit of the dividend next to the remainder of the subtraction.
• Repeat: Repeat steps 2-4 until all digits of the dividend have been used, or you have reached your desired level of precision.
• Decimal Placement: If the dividend has a decimal, you'll bring the decimal point straight up into the quotient when you reach the decimal place in the dividend.
• Decimal Divisor: If the divisor has a decimal, move the decimal point in both the divisor and the dividend to the right until the divisor becomes a whole number. This will result in an equivalent division problem that is easier to calculate.

Example

Let's work through a specific example: dividing 12.6 by 3.

1. Setup:

       ______
   3 | 12.6

2. Initial Division: 3 goes into 12 four times.

        4___
   3 | 12.6

3. Multiply and Subtract: 4 * 3 = 12. Subtract 12 from 12.

        4___
   3 | 12.6
       -12
        ---
         0

4. Bring Down: Bring down the 6.

        4___
   3 | 12.6
       -12
       ---
        06

5. Decimal Placement: We've reached the decimal place in the dividend so carry up the decimal into our quotient.

        4.___
   3 | 12.6
       -12
       ---
        06

6. Repeat: 3 goes into 6 twice.

        4.2_
   3 | 12.6
       -12
       ---
        06
       - 6
       ---
        0

Therefore, 12.6 divided by 3 equals 4.2.

Practical Insights

• Estimation: Before diving into the detailed calculation, try to estimate the result. This helps in checking the reasonableness of your answer.
• Remainders: If the division does not come out evenly, you can continue to add zeros after the decimal point of the dividend to get a more precise answer.
• Calculators: For complex calculations, utilizing a calculator is appropriate to ensure precision.
• Fractions: Double numbers can be converted into fractions and divided as well, sometimes simplifying the process depending on the values.

Handling Decimal Divisors

Let's illustrate handling decimal divisors with 12.6 / 0.3 as an example:

1. Adjust: Move the decimal point one place to the right in both the divisor and dividend:

   • 0.3 becomes 3
   • 12.6 becomes 126

   Our new problem is 126 / 3.

2. Divide: 126 / 3 = 42

Therefore, 12.6 / 0.3 = 42.