<p>Multiplication of Decimals In this section, we will consider the multiplication of a decimal by a whole number, multiplication of a decimal by a power of ten, multiplication of a decimal by a multiple of a power of ten and multiplication of a decimal by another decimal. </p><p>Multiplication of a Decimal by a Whole Number</p><p>Multiplication is repeated addition.</p><p>This can be represented on the number line as follows:</p><p>Note the following:</p><p>This suggests that:</p><p>To multiply a decimal number by a whole number:</p><p> ignore the decimal point and multiply the digits  place the decimal point in the answer so that it has the same number of decimal places as the number being multiplied </p><p>Example 11</p><p>Calculate 45.27 × 6.</p><p>Solution: Note:</p><p>There are two decimal places in the decimal number being multiplied. So, we place the decimal point two places from the right-hand end of the answer.</p><p>Example 12</p><p>Calculate 7.382 × 5.</p><p>Solution:</p><p>Note:</p><p> There are three decimal places in the decimal number being multiplied. So, we place the decimal point three places from the right-hand end of the answer.  Any trailing zeros in the decimal places of the answer can be omitted. </p><p>In general:</p><p>If there are n decimal places in the decimal number being multiplied, then place the decimal point n places from the right-hand end of the answer.</p><p>Example 13</p><p>Calculate 0.0005 × 8.</p><p>Solution: Note:</p><p> There are four decimal places in the decimal number being multiplied. So, we place the decimal point four places from the right-hand end of the answer.  Any trailing zeros in the decimal places of the answer can be omitted. </p><p>Example 14</p><p>Calculate 47.4 × 45.</p><p>Solution:</p><p>Note:</p><p> There is one decimal place in the decimal number being multiplied. So, we place the decimal point one place from the right-hand end of the answer. </p><p> Any trailing zeros in the decimal places of the answer can be omitted</p><p>Multiplying thousandths by tenths How to multiply a three digit decimal by a one digit decimal number (for example 0.529 * 0.7): </p><p>Place one decimal above the other so that they are lined up on the right side. Draw a line under the bottom number. Temporarily disregard the decimal points and multiply the numbers like multiplying a three digit number by a one digit number. </p><p>0.529 0.7</p><p>Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger than 10 so place a six above the center column and place three below the line in the right column. </p><p>6 0.529 0. 7 3</p><p>Multiply the digit in the top center column (2) by the digit in the center of the right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The units place value (0) of 20 is placed below the line and the tens place value (2) of the 20 is placed above the five. </p><p>26 0.529 0. 7 03</p><p>The five of the top number is multiplied by the seven of the multiplier (5*7=35). The two that was previously carried is added and 37 is placed below the line. At the start we disregarded the decimal places. We must now count up the decimal places and move the decimal place to its proper location. We have three decimal places in 0.529 and one in the decimal 0.7 so we move the decimal four places to the left to give the final answer of 0.3703. </p><p>26 0.529 0. 7 0.3703</p>