Multiplying Decimals

The Big Idea:

To multiplying decimals, just ignore the decimal and multiply like normal. Then re-insert the decimal in the correct spot.

1.  Multiply the numbers just as if they were whole numbers.
     (do not align the decimal points)

2.  Place the decimal

     a. Using a reasonable estimate method:
 
     (one of the most common errors made in multiplying decimal numbers is in misplacing the decimal point in the answer. Determining what a reasonable answer would be before multiplying usually prevents this error.)
 
     Estimate the product then use that estimation to place the decimal point in the answer.

Example:     $34.5∗20.5$
$345∗205=70725$
Think:     $20$ times $35$ would be $700$.
The answer should be around 700:     $34.5∗20.5=707.25$

 
     b. Counting Decimal Places method:

     • Count the decimal places to the right of the decimal points in each of the original numbers.
     • Then put the decimal point in the answer – it will have as many decimal places as the two original numbers combined.
     • Start at the right-most digit of the product. Move the decimal point to the left the necessary number of decimal places.
     

Example:     $3.4∗0.78$
$34∗78=2652$
Think:   There is 1 decimal place in     3.4.
There are 2 decimal places in     0.78
$1+2=3$          
So there are 3 decimal places in the product.    multiplying decimals
So count over from the right to get     $3.4*0.78=2.652$

 
Some times you need to add zeros to the left of the number:

Example:     $0.03 ∗ 1.1$    (total of 3 decimal places in the product)
$3 ∗ 11 = 33$
    $0.03 ∗ 1.1 = 0.033$