We're lucky! In our "electronic age," people use a calculator most of the time to multiply and divide decimal numbers. It's important, however, to learn to do these calculations by hand. It's easy to push a wrong button on a calculator and think a wrong answer is right, if you have no idea how the answer is found! Besides, a calculator is not always handy when you need it.

Here are the rules for multiplying decimal numbers:

1. Multiply the numbers just as if they were whole numbers:

• Line up the numbers on the right--do not align the decimal points.
• Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
• Add the products.

2. Place the decimal point in the answer by starting at the right and moving the point the number of places equal to the sum of the decimal places in both numbers multiplied.

Example

37.7 x 2.8 = ? --->

     37.7     ( 1 decimal place )
   x  2.8     ( 1 decimal place )
  3016
+754  
105.56       ( 2 decimal places, move point 2 places left )

Hint: Use estimating to help you check the placement of the decimal point. You could round 37.7 to 40 and 2.8 to 3. It's easy to multiply 3 x 40 so you know your answer should be close to 120.

Here's a "mental math" shortcut: When multiplying a number by a multiple of ten, just move the decimal point one space to the right for every zero.

10 x 0.6284 = 6.284 (1 zero, 1 space right)
100 x 0.6284 = 62.84 (2 zeroes, 2 spaces right)
1000 x 0.6284 = 628.4 (3 zeroes, 3 spaces right)
10,000 x 0.6284 = 6284 (4 zeroes, 4 spaces right)
100,000 x 0.6284 = 62,840 (5 zeroes, 5 spaces right)

Example

1. Find the product of    9.683 x 6.1 = ?

   Line up the numbers on the right, multiply each digit in the top number by the each digit in the bottom number (like whole numbers), add the products, and mark off decimal places equal to the sum of the decimal places in the numbers being multiplied.

        9.683    ( 3 decimal places)
        x  6.1   ( 1 decimal place)
         9683   (1 x 9683)
   + 58098     (6 x 96830)
      59.0663  (3 + 1 = 4 decimal places)

2. Jackie just bought a new convertible. How far will she get on the highway before she runs out of gas and has to call a tow truck?

   First, estimate your answer to the tens place. Then make an exact calculation, using the calculator.

   Estimate:

   24.5 -> 20 15.2 -> 20 20 x 20 = 400 miles

   Exact calculation:

24.5 x 15.2 = 372.40

You can drop the trailing zero in a decimal number. For example, 372.40 is the same as 372.4. This is because the ".40" part of the number is the same as ".4". This is the same as saying that 40/100 is the same as 4/10.

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