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.
|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.
|Think: There is 1 decimal place in||3.4.|
|There are 2 decimal places in||0.78|
|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)|
|$3 ∗ 11 = 33$|
|$0.03 ∗ 1.1 = 0.033$|