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)
$3 ∗ 11 = 33$
$0.03 ∗ 1.1 = 0.033$