Notes 6 – 4 Day 1 Scientific Notation
Date ________
Algebra 1
Objective: At the end of this lesson, students will be able to express a number in scientific
notation.
Have you ever used scientific notation before? Where? What is scientific notation used
for?
Speed of Light – approximately 290,000,000 meters per second
Diameter of an Atom – approximately 0.00000001 centimeters
Scientific Notation – a x 10n, where 1  a < 10 and n is an integer
Example 1 – Express 106,000 in scientific notation.

Step 1 – Find the decimal point. If it is not written in the number, write it in.

Step 2 – Find a.
o Figure out where the “new” decimal point must be for scientific notation.

Since 1  a < 10, there can only be one digit in front of (to the left of)
the decimal point.
o Any zeros after the last non-zero number can be dropped.

Step 3 – Find n.
o Count how many spaces you are moving the decimal point. This gives you n,
which is the exponent.
o Figure out the direction you are moving the decimal point. This tells you the
sign (positive or negative) of the exponent.


When you move the decimal to the left, you will have a positive exponent.

When you move the decimal to the right, you will have a negative exponent.
Step 4 – Write your answer in scientific notation.
o Fill in the value of a and n into
a x 10n
Something to keep in mind when working with scientific notation:

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.
Example 1 – Write the following in scientific notation.
a. 290,000,000
b. 0.00000001
c. 0.00390
d. 4,293
e. 0.01234
e. 319,000
Look at the examples below. Are they in scientific notation? Why or why not?
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Example 2 – Write the following in scientific notation.
a. 32,000 x 103
b. 0.00031 x 102
c. 0.025 x 10-2
d. 777 x 10-5