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) |
| $3 ∗ 11 = 33$ | ||
| $0.03 ∗ 1.1 = 0.033$ |
