How+to+Multiple+and+Divide+with+Decimals

Dividing a Decimal Number by a Whole Number
Source: [|Math is Fun] To divide a decimal number by a whole number:
 * Use [|Long Division] (ignoring the decimal point)
 * Then put the decimal point in the same spot as the dividend (the number being divided)

Example: Divide 9.1 by 7
Ignore the decimal point and use Long Division: __13__ 7 )9.1  9  __7__  21  __21__  0  ||

Put the decimal point in the answer directly above the decimal point in the dividend: || __1.3__ 7 )9.1  ||

The answer is 1.3

Dividing by a Decimal Number
But what if you want to divide **by** a Decimal Number? The trick is to convert the number you are dividing by to a whole number first, by **shifting the decimal point of both numbers** to the right: Now you are **dividing by a whole number**, and can continue as normal. It is safe to do this if you remember to shift the decimal point of **both numbers** the same number of places.

Example 2: Divide 5.39 by 1.1
You are **not** dividing by a whole number, so you need to move the decimal point so that you **are** dividing by a whole number: |||||| move 1 ||


 * **5.39** || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **53.9** ||
 * **1.1** || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **11** ||
 * move 1 ||

You are now dividing by a whole number, so you can proceed: Ignore the decimal point and use Long Division: || __049__ 11 )539  5  __0__  53  __44__  99  __99__  0  ||

Put the decimal point in the answer directly above the decimal point in the dividend: || __04.9__ 11 )53.9  ||

The answer is 4.9

=Multiplying Decimals= //Multiply without the decimal point, then re-insert it in the correct spot!//

How to Multiply Decimals
Just follow these steps: In other words, just count up how many numbers are after the decimal point in //both// numbers you are multiplying, then the answer should have that many numbers after //its// decimal point.
 * Multiply normally, ignoring the decimal points.
 * **Then** put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

Example: Multiply 0.03 by 1.1
and 1.1 has **1 decimal place**, so the answer has **3 decimal places**: ||  ||~ 0.033 ||
 * start with: ||  ||~ 0.03 × 1.1 ||
 * multiply without decimal points: ||  ||~ 3 × 11 = 33 ||
 * 0.03 has **2 decimal places**,


 * [[image:http://www.mathsisfun.com/images/style/animation.gif width="70" height="43" caption="animation"]] || See the [|Multiplying Decimals Animations] ||

How Does It Work?
Because when you multiply without the decimal point (which makes it easy), you are really shifting the decimal point to the right to **get it out of the way**:
 * //Original:// ||  || //1 Move:// ||   || //2 Moves:// ||   || //3 Moves:// ||
 * 0.03 × 1.1 || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **0.3** × 1.1 || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **3.** × 1.1 || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **3.** × **11.** ||

Then we do the (now easy) multiplication: 3. × 11. = 33. But remember, we did 3 Moves of the decimal point, so we need to undo that: Here are some more examples:
 * //3 Moves:// ||  || //2 Moves:// ||   || //1 Move:// ||   || //Correct// ||
 * **33.** || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **3.3** || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **0.33** || [[image:http://www.mathsisfun.com/images/arrow.gif width="30" height="30"]] || **0.033** ||

Example: Multiply 0.25 by 0.2
and 0.2 has 1 decimal place, so the answer has 3 decimal places: ||  ||~ 0.050 ||
 * || start with: ||  ||~ 0.25 × 0.2 ||
 * || multiply without decimal points: ||  ||~ 25 × 2 = 50 ||
 * || 0.25 has 2 decimal places,

Example: Multiply 102 by 0.22
and 0.22 has 2 decimal place, so the answer has 2 decimal places: ||  ||~ 22.44 || As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor do you want to get only one-tenth of what you need! And that's all. Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.
 * || start with: ||  ||~ 102 × 0.22 ||
 * || multiply without decimal points: ||  ||~ 102 × 22 = 2,244 ||
 * || 102 has 0 decimal places,