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
Make up your own rule below to help you remember how to write in 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
Make up your own rule below to help you remember how to write in 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
Here's the "official” rule for writing in scientific notation, 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. Note
that after you move the decimal you only need to write the first digit, then the new decimal point and the
tenths and hundreds digits. Some teachers might want you to write more digits, but not in my class.
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 2 x 5.67 x 109. 5.67 x 2 = 11.34.
So our answer is 11.34 x 109. But we're not done. First notice that when we multiply we don't multiply the
exponent, only the number in front before the exponent. 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
109+1 = 1010. Our exponent is now 1010. Now we are done! Remember you only have to write the first
part of the number as 1.13 not 1.134, in other words only write the one's, tenths and hundreds digits.
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