# 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 × 10^{3} * 8 × 10^{2} = 7*8 (plus 5 zeros) = 56 × 10^{5}

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 × 10^{5} / 7 × 10^{3} = 56/7 (with (5-3) zeros)

= 8 × 10^{2} .

### There are 200 children in an elementary school, and each one brings 3.1 × 10^{6}
germs. How many germs is that?

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

- I need a hint ... : 200 = 2 * 10
^{2}.

- ...another hint ... : 2 × 10
^{2}* 3.1 × 10^{6}= ?

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

#### I think I have the answer: 6.2 × 10^{8} , or 620 billion.

...and...

### The Health Department estimates that a school contains 9 * 10^{12} 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 × 10
^{12}/ 2 × 10^{2}= ?

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

#### I think I have the answer: 4.5 × 10^{10} , or 45 billion per child.

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