Exponents, square roots, and scientific
notation
Solve:
5 x 102 =
4 x 104 =
Scientific notation:
Remember this?
102 = 100
10 3 = 1000
Well, here is the next step:
4 x 102 = 4 x 100 = 400
6 x 103 = 6 x 1000 = 6000
So…what about this?
Solve:
6.5 x 102 =
7.2 x 103 =
5.5 x 102 = 5.5 x 100 = 550
Notice what happened:
The decimal moved over 2 places
2
4.3 x 10 =
because of the 2 zeros in 100.
One more time:
3.5 x 103 = 3.5 x 1000 = 3500 because
there are 3 zeros in 1000 so you move
the decimal over 3 places.
Write a number in scientific notation.
3.5 x 103 is called scientific notation.
Write the same number in expanded
form.
3500 is called expanded form.
Write this in scientific notation:
4, 400,000
Now let’s go backwards.
5,700,000
Write this in expanded form:
4.2 x 102
Let’s write this in scientific notation:
5.7 x 106
Move the decimal until you create a
Write this in expanded form:
7.3 x 104
number between 1 and 10. Count the
number of decimal places. Rewrite the
number you created and multiply it by 10 to how
many places you moved the decimal.
Write this in expanded form:
8.5 x 103
Notice the number of decimal places
I moved. 5 zeros plus the 7 = 6 places.
Write this in scientific notation:
.000004
Remember what we learned yesterday?
Negative exponents?
Write this in scientific notation:
.000055
If you have a negative exponent you move the
other way!
8.5 x 10−3 = 0.0085
Write this in expanded form:
8.5 x 10-3
What if you have 0.067 and want to make it into
scientific notation?
Move them decimal to the right 3 spaces to make 6.7
Write this in expanded form:
7.3 x 10-4
Summary:
then multiply it by 10 to the -3, you are done!