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.
I think I have the answer: 6.2 × 108 , or 620 billion.
...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.
I think I have the answer: 4.5 × 1010 , or 45 billion per child.
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