Multiplying and dividing decimals by 10, 100 and 1000
In a nutshell
Decimal numbers are numbers with digits which are not zero after a decimal point. To multiply or divide decimals by $10,100,1000,$ you must use place values to move the decimal place a certain number of places to the left or right.
Multiplying decimals by 10, 100, 1000
To multiply decimals by $10,100,1000$, follow this procedure:
PROCEDURE
$\times10$
 Move the decimal point one place to the right.

$\times 100$
 Move the decimal point two places to the right.

$\times 1000$
 Move the decimal point three places to the right.

Example 1
Calculate $2.25 \times 1000$.
Identify the multiplier.
$2.25 \times \underline{1000}$
Move the decimal point three places to the right.
$2.\overset{\curvearrowright\,\,\,\,\,}{2\thinspace 5 \thinspace}$
$2.\overset{\curvearrowright\,\curvearrowright\,\,\,\,}{2\thinspace 5 \thinspace 0}$
$2.\overset{\curvearrowright\curvearrowright\curvearrowright\,\,\,}{2\thinspace 5 \thinspace 0\thinspace0}$
Complete the multiplication.
$\underline{ 2.25 \times 1000 = 2250.0 = 2250}$
Note: $0$ is a placeholder which is used if you reach the end of a decimal number. If a $0$ is at the very end of a decimal it can be removed from the final answer.
Dividing decimals by 10, 100, 1000
To divide decimals by $10,100,1000$, follow this procedure:
PROCEDURE
$\div10$
 Move the decimal point one place to the left.

$\div100$
 Move the decimal point two places to the left.

$\div1000$
 Move the decimal point three places to the left. 
Example 2
Calculate $422.5 \div100$.
Identify the number you are dividing by.
$422.5 \div \underline{100}$
Move the decimal point two places to the left.
$42\overset{ \curvearrowleft}{2\thinspace }.5$
$4\overset{\curvearrowleft \curvearrowleft}{2\thinspace 2 }.5$
Complete the division.
$\underline{422.5 \div 100 = 4.225}$
Note: Only the decimal point moves position when dividing by $10,100,1000$.