Decimals

When multiplying decimals, the decimal points do not have to be aligned. Rather, it is important to accurately position the decimal point in the product. To position the decimal in the product, the total number of digits to the right of the decimals in the numbers being multiplied must be equal to the number of digits to the right of the decimal in the product. This is best illustrated in the following examples:

Step 1:Multiply numbers without inserting decimal in the products.

Step 2:Sum the number of digits to the right of the decimal in all of the numbers being multiplied.

Step 3:Position the decimal in the product so the number of digits to the right of the decimal equals the total number of digits to the right of the decimal in the numbers multiplied (from Step 2).

Example:

Solution:

NOTE:Since 0.056 has three digits to the right of the decimal point, and 0.032 has three digits to the right of the decimal point, six digits must be to the right of the decimal point in the product. To have six digits in the product, zeros are inserted to the left of the computed digits.

To multiply a decimal by 10, move the decimal point one position to the right.

Example: 0.45 x 10 = 4.5. Similarly, when multiplying a decimal by 100, 1000, and 10,000, move the decimal point to the right the same number of zeros that are in the multiplier.

Example:

The reverse is true when multiplying by fractions of 10.