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Long division is a method used to divide large numbers by breaking them down into simpler steps. It involves setting up a problem in a specific format where the dividend is placed under a division bracket, and the divisor is placed outside. This structure helps us systematically find the quotient.

In our exercise, we are dividing 19.80 by 396. To start, we write the problem using long division format: place 19.80 under the division bar and 396 outside. This setup allows us to visually break down the division into manageable parts, tackling them one at a time. By focusing on dividing numbers within place values, long division helps handle both whole numbers and decimals effectively.

Normalizing decimals is a technique used to simplify division when decimals are present. The goal is to transform the division into an equivalent problem without decimals, making the calculation easier. This means removing the decimals by multiplying both the dividend and the divisor by the same power of ten.

In the example of dividing 19.80 by 396, there are two decimal places in 19.80. To normalize, we multiply both 19.80 and 396 by 100, moving the decimal point two places to the right. Consequently, the division becomes 1980 divided by 396, which is simpler to handle as it now involves only whole numbers. Normalizing prevents decimal confusion and allows straightforward manipulation of the numbers involved.

Performing division involves a clear and orderly process that includes several steps to ensure accuracy. After normalizing the decimals, the next step is to perform the actual division using long division.

First, estimate how many times the divisor fits into the current section of the dividend. In our case, 396 fits into 1980 exactly 5 times because 396 multiplied by 5 equals 1980. You then write the number 5 above the division bar as the quotient.

• Calculate by multiplying your quotient by the divisor to check accuracy: 5 times 396 equals 1980.
• Subtract this product from the dividend: 1980 minus 1980 leaves no remainder, confirming the division is complete.

By following these steps, you maintain the integrity of the calculation and easily arrive at the correct decimal result.