More on Dividing by Powers of Ten

When you divide a decimal number by 10, 100, 1000, etc., the number gets smaller.

ones	$\bullet$ tenths	hundredths	thousandths	ten-thousandths
$\color{red}{3}$	$\color{red}{\bullet\;\; 1}$	$\color{red}{2}$			$\color{red}{\longleftarrow 3.12}$
$0$	$\bullet$ $3$	$1$	$2$		$\color{red}{\longleftarrow 3.12\div 10 = 0.312}$
$0$	$\bullet$ $0$	$3$	$1$	$2$	$\color{red}{\longleftarrow 3.12\div 100 = 0.0312}$

The table shows that when you divide a number by $10, 100, 1000$, etc., the number gets smaller so move the digits to the right.

In practice the easiest way to divide by $10, 100, 1000$, etc. is to move the decimal point to the left.

dividing by $\color{red}{10}$, the digits stay the same but the decimal point moves one place to the right
dividing by $\color{red}{100}$, the digits stay the same but the decimal point moves two places to the right
dividing by $\color{red}{1000}$, the digits stay the same but the decimal point moves three places to the right
and so on.

So the decimal point moves to the left by the number of places that matches the number of zeros in the number you are dividing by.

Try these problems to test your understanding: