Notes 6 – 4 Day 2 Scientific Notation
Date ________
Algebra 1
Objective: At the end of this lesson, students will be able to

multiply and divide numbers in scientific notation.

change a number in scientific notation to decimal notation.
In 6 – 4 Day 1, we learned how to change a decimal number into scientific notation.
Today we are going to go the other direction – change a number in scientific notation to
decimal notation.
Remember:

A BIG number (like 700,000,000,000,000) will have a POSITIVE exponent.

A SMALL number (like 0.0000000000007) will have a NEGATIVE exponent.
Since 3.4 x 104 has a positive exponent, it will be a BIG number. To change it to decimal
notation, we would have to move the decimal to the ___________________
How many places do we move the decimal? ____________________
Since 1.8 x 10-2 has a negative exponent, it will be a SMALL number. To change it to
decimal notation, we would have to move the decimal to the ___________________
How many places do we move the decimal? ____________________
Example 1 – Express each number in decimal notation.
a. 2.0 x 10-3
b. 6.05 x 10
c. 4.6656 x 10-2
d. 3.3 x 103
Now we are going to put EVERYTHING together – multiplying monomials, dividing
monomials and scientific notation. Let’s use problems we already know how to do to help
us with something that looks new!
Example 2 – Simplify.
a. (5a2)(4a3)
c.
9b 6
3b 2
b. (5 x 102)(4 x 103)
d.
9 x 10 6
3 x 10 2
For Example 3, we’re just combining Examples 1 & 2!!
Example 3 – Evaluate. Express each result in decimal notation.
1.17 x 10 7
a.
5 x 10 2
c.
1.68 x 10 4
8.4 x 10 4
b. (8.3 x 102)(9.1 x 10-7)
d. (3.8 x 10-6)(1.9 x 106)
Example 4 – Express each result from Example 3 in scientific notation.
a.
b.
c.
d.