Scientific Notation - Download as DOC - DOC

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					Scientific Notation
The Universe is both very big and very small. So scientists need a way to write big and small numbers
without running out of paper. For example, try writing 1 google. That’s 1 with 100 zeros! Try writing 1
google.

How many zeros did you write before you gave up? ______
If you use scientific notation then it’s easy to write: 1 google = 10100.

Scientific notation is easy to learn. Here are some examples of scientific method with big numbers.
100 = 1
101 = 10
102 = 100
103 = 1000
104 = 10,000

Write a rule to help you remember how to write scientific method for big numbers:


Here are some examples of scientific method with small numbers:
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
10-4 = 0.0001
10-5 = 0.00001

Write a rule to help you remember how to write scientific method for small numbers:


How do you write numbers like 234, or 579,000,000, or 0.0000897?
Here they are:

2.34 x 102
5.79 x 108
8.97 x 10-5

For large numbers move the decimal point to the right of the first digit, count the number of places you
moved the decimal and multiply that number times 10 to the power of (an exponent) the number of places
you moved the decimal. For small numbers, move the decimal place to the right of the first significant digit
(the first digit that is not zero from the left) and multiply that number by ten to the power of the negative
number of places you moved the decimal

Write the following numbers in scientific notation on the back of this paper:
143,000,000 0.00000987 363,483,499,000,000 0.0057 398,900 0.67000000000001

Now let's multiply a number in scientific notation by 2. Let's multiply 5.67 x 10 9. Multiply 5.67 x 2 =
11.34. The number multiplied times 2 is 11.34 x 10 9. But we're not done. First though notice that when
we multiply by 2 we don't do anything to the exponent, it just tags along with the first part of the number
itself: 5.57). OK, now let's write our answer again. It was 11.34 x 109. 11.34 is not in proper scientific
notation form. Recall that we always move the decimal to the right of the first significant digit. So move
the decimal from 11.34 to 1.134. OK, good. But since we moved the decimal one place to the left we need
to add that movement of one place to the exponent. So 10 9+1 = 1010. Our exponent is now 1010. By the
way, we only have to write the first part of the number as 1.13 not 1.134, but we'll save that for another
lesson.

Multiply the following numbers and write the answers on the back!
3.45 x 105 x 3     5.8 x 1017 x 4  3.56 x 108 x 5    2.98 x 108 x 6         8.45 x 107 x 8    3.45 x 10-3 x 2

				
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posted:6/23/2012
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