# 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. 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) $3 ∗ 11 = 33$ $0.03 ∗ 1.1 = 0.033$