MTH60 Day 10 Section 3.1, Review for Proficiency Test
Section 3.1
Scientific Notation
How many are in some type of science class? Scientific notation is used a lot in the sciences but it is in
other fields also. Reading very large or very small numbers can be difficult; it is easy to miss a zero.
First, review exponents: x3 =
x is the base and 3 is the exponent.
With scientific notation we are working with exponents whose base is 10:
103=
109 =
etc.
Population of the US is about 310,000,000 people. The population of the Portland metro area is about
1,800,000 people. These numbers are in standard notation.
Scientific notation is always a number between 1 and 10 multiplied by a power of 10:
5000 = 5 x 1000 = 5 x 103
40,000,000 = 4 x 10,000,000 = 4 x 107
1,800,000 = 1.8 x 1,000,000 = 1,8 x 106
310,000,000 = 3.1 x 100,000,000 = 3.1 x 108
Anyone know the shortcut for figuring out the exponent on these?
Why are the following NOT in scientific notation?
42.3 x 106
0.6 x 103
1.2 x 83
How can we convert a number in scientific notation back to standard notation?
5.3 x 107 =
How about very small numbers? Such as 0.000 002, etc.
This is something you will have to take on faith for now, but we can write very small numbers in
scientific notation using negative exponents. Just think about how many decimal places you need to
move to get a number between 1 and 10, that will be the exponent of the 10 but we make it a negative
exponent to distinguish that it is a small number, not a large number.
5,000,000 = ___________
while
0.000 005 = _______________
Do NOT think in terms of the number of zeroes. Think in terms of the decimal places you move.
More examples….
Are the following large numbers or little numbers?
Examples….
One of the reasons that scientific notation was developed has to do with the fact that we didn’t used to
have calculators. (They appeared in the 1970’s) If numbers are in Scientific Notation it is relatively easy
to multiply them by hand (without messing up the 0’s!)
X2 *x3 = x*x*x*x*x = x5, in general if you multiply two numbers with the same base you can add the
exponents and keep the common base.
103 * 106 =
10-3 x 106 =
So to multiply (3 x 104)* (4 x 10-2) =
Notice we are not in scientific notation any longer, but we can fix that: how many places do we need to
move the decimal?
Is it OK that we moved the numbers around? Yes, multiplication (and addition) is commutative. So we
can change the order without changing the result.
More examples (feel free to use your calculators as needed).
Applications:
Cholera is a disease spread by bacteria. The size of one is 6.9kB. a kB is 1000 bp and a bp is one-ten
billionth meter. 6.9 x 103 x 10-10 =
Need to ingest 1 million to 100 million of these bacteria to get sick, depending on the acidity of your
stomach.
100 million in a row would be 108 x 6.9 x 10-7 m =
For water to look cloudy would need to be concentrated at 10 million bacteria per milliliter