Multiplying Decimals

Multiplying Thousandths by Hundredths

Multiplying a three digit decimal by a two decimal number (for example 0.529 * 0.67) involves several steps.

• 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 you would multiply a three digit number by a two digit number.

0.529
 0.67

• 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.

   6
0.529
 0.67
    3

• Multiply the digit in the top center column (2) by the digit in the lower right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The 0 of 20 is placed below the line and the 2 of the 20 is placed above the five.

  26
0.529
 0.67
   03

• The five of the top number is multiplied by the seven of the lower multiplier (5*7=35). The two that was previously carried is added and the 37 is placed below the line.

  26
0.529
 0.67
 3703

• After 529 has been multiplied by seven as shown above, 529 is multiplied by the six of the multiplier. The number is moved one place to the left. The result would be 3174:

   15
 0.529
  0.67
  3703
 3174

• A line is drawn under the lower product (3174) and the products are added together to get the final answer of 35443. At the start we disregarded the decimal points. 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 two in the decimal 0.67 so we move the decimal five places to the left to give the final answer of 0.35443.

  
      15
    0.529
     0.67
     3703
    3174
  0.35443