Powers of $10$ refer to $10, 100, 1000$ and so on. To multiply and divide by powers of $10$, you have to use place values to move the decimal place a certain number of steps to the left or right.

Multiplying by powers of 10

To multiply by powers of $10$, follow this procedure:

procedure

Count how many zeros there are in the power of $10$.

Move the decimal point to the right by the same amount.

Note: If the number is a whole number, then add "$.000...$", adding as many zeros as required.

Example 1

What is $3.2\times1000$?

First, count how many zeros are in $1000$. Then, write $3.2$ as $3.2000..$ and move the decimal point $\textbf{3}$ places to the right. Finally, get rid of the extra zeros past the decimal point.

Dividing by powers of 10

To divide by powers of $10$, it is exactly the same as multiplying, except the decimal point moves the other way.

procedure

Count how many zeros there are in the power of 10.

Move the decimal point to the left by the same amount, adding zeroes to the left if necessary.

Example 2

What is $25\div100000$?

First, count how many zeros there are in $100000$. Then, write $25$ as $...000025.0$, and move the decimal point 5 places to the left. Get rid of the unnecessary zeros.

Multiplying and dividing by multiples of powers of 10

Multiples of powers of $10$ refers to numbers such as: $30000, 20, 800$ and so on. To multiply and divide by these numbers, first you have to multiply or divide by the multiple (the number "attached" to the power of $10$).

Example 3

What is $400\div50000$?

First, write $50000$ as $5\times10000$.

To compute $400\div50000$, first do $400\div5$ and then divide the answer by $10000$, using the method above: