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## Multiplying Decimals

#### Introduction

Multiplying decimals is very similar to multiplying whole numbers, although special attention needs to be given to the position of the decimal point.

#### Terms

Decimal Point - The decimal point looks like a period and is always placed after the “ones” position of a number.
Decimal Notation - Decimal notation is useful for writing numbers which are not whole numbers.
Whole Number - A whole number is a number with nothing but zeroes after the decimal point.

## Lesson

The most important thing to remember about multiplying decimals is to make sure that the decimal place is in the right spot. You may think at first that

$.02 * .03 = .06$ but the correct answer is actually $.0006$.

To multiply two decimals, first count the number of digits each number has after the decimal point. For example, .02 has two digits after the decimal point, .0034 has four digits, and .9999999 has 7 digits.

Next, forget about the decimal place and multiply the two numbers as if they were normal whole numbers. Finally, when finished, add up the number of digits each number had originally; your final answer should have that many digits after the decimal.

For example, let’s calculate $.0005 * .02$. The number .0005 has four digits after the decimal and .02 has two digits. This means that our final answer will have $4+2=6$ digits after the decimal point. Next, multiply the two numbers as if there were no decimal place at all. $2 * 5=10$ Finally, move the decimal place six digits to the left, and we are left with our final answer, .000010, which can be simplified as .00001.

## Examples

#### Multiplying Decimals (Example 1)

$2.5 * 1.4$
 2 5 * 1 4 1 0 0 + 2 5 0 3 5 0
$2.5 has one digit after the decimal$
$1.4 has one digit after the decimal$
We move the decimal point $2$ ($1$+$1$) places to the left

#### Multiplying Decimals (Example 2)

A taxi driver charges \\$3.74 permile. How much does Brandon pay if he travels 14.07 miles?

#### Multiplying Decimals (Example 3)

$2.5 * 3$
 1 2 5 * 3 + 7 5 7 5