# Detour: Multiplying and Dividing Scientifically

Somewhere along the line, you probably learned the "rule of 10" -- to multiply two numbers that are followed by zeros, you need to multiply the numbers (without zeros) then add the total number of zeros, like this:

7000*800 = 7*8 (plus 5 zeros) = 5,600,000

Well, scientific notation works EXACTLY the same:

7 × 103 * 8 × 102 = 7*8 (plus 5 zeros) = 56 × 105

In shorthand: multiply the numbers, add the zeros.

Division is similar -- divide the numbers, subtract the zeros:

5,600,000 / 7000 ... cancel 3 zeros ...
5600/7 = 800

56 × 105 / 7 × 103 = 56/7 (with (5-3) zeros)
= 8 × 102 .

### There are 200 children in an elementary school, and each one brings 3.1 × 106 germs. How many germs is that?

(To make this problem interactive, turn on javascript!)

• I need a hint ... : 200 = 2 * 102.

• ...another hint ... : 2 × 102 * 3.1 × 106 = ?

• ...another hint ... : Multiply the numbers, add the zeros.

...and...

### The Health Department estimates that a school contains 9 * 1012 germs. How many germs is that per child (200 kids in the school)?

(To make this problem interactive, turn on javascript!)

• I need a hint ... : 9 × 1012 / 2 × 102 = ?

• ...another hint ... : divide the numbers, subtract the zeros.