Multiplication and Division with Decimals

**Multiplication and Division with Decimals**

**Multiplication with Decimals**

Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product.

0.7 0.352 = 2464 (*now you need to place the decimal point in the produc*t)

To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.

0.7 1 decimal place

0.352 3 decimal places

A total of 4 decimal places

Once you have found the sum of the decimal places in each factor, you know how many decimal places the product will need after its decimal point. Starting at the far right of the number, move the decimal point toward the left that number of decimal places.

0.2464 (4 decimal places after the decimal point)

**Example**

Solve: 0.9 × 0.3

**Solution**

First multiply ignoring the decimal points

3 9 = 27

Then place the point in the product (*in this case, two decimal places*)

27 => 0.27

0.3 0.9 = **0.27**

If necessary, add zeros to the left side of the product.

**Example(2)**

Solve: 0.05 0.4

Solution

Multiply as you would whole numbers, ignore decimal places

0.05

__ 0.4__

20

Count the number of decimal places needed for the product

0.05 2 decimal places

__ 0.4__ 1 decimal place

20 A total of 3 decimal places

Write zeroes in front of the whole number to place the decimal point correctly

0.05

__ 0.4__

0.020

Therefore 0.05 0.4 = **0.02**

**Dividing Decimals**

1. Move the decimal point in the divisor to the right to make the divisor a whole number.

2. Move the decimal point in the dividend the same number of places to the right.

3. Place the decimal point in the quotient directly over the decimal point in the dividend for the final quotient.

4. Divide as if working with whole numbers

At times, it may be necessary to round a quotient to a given place value.

**Example**

Solve and round to the nearest hundredth: 1.5 0.45

Since 3 < 5, rounding the answer we obtain: 1.5 0.45 = **3.33**

**Decimals with Exponents**

A decimal with exponents is simply the decimal multiplied by itself *n* times, where *n* is the value for the exponent.

**Example**

Evaluate the following expressions.

1.) (0.6)^{2} = 0.6 0.6 = **0.36**

2.) (0.6)^{3} = 0.6 0.6 0.6 = 0.36 0.6 = **0.216**