SCIENTIFIC NOTATION
Standard:
M8N1: Students will understand different representations of numbers including square roots, exponents, and scientific notations.
i. Simplify expressions containing integer exponents.
j: Express and use numbers in scientific notation.
k: Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation.
Student will understand:
vocabulary related to the standard and needed to complete the performance task.
Lesson objectives
Teachers' notes
1
Subject: Mathematics
Topic: Scientific Notation
Grade(s):
8th
Prior knowledge: Exponents as evaluated expressions and
formulas, perfect square numbers, rational
numbers, including negative rational numbers,
and irrational numbers.
Created by: Kimberly Williams
Lesson notes:
See the attachments tab for the complete unit framework.
Lesson objectives
Teachers' notes
2
SCIENTIFIC NOTATION
... is a way to express very small or very
large numbers.
Scientific Notation is used most often in
"analysis" work where precision is
important.
3
Scientific Notation consists of two parts:
1) a number between 1 and 10, such
that 1<n<10
and
2) a power of 10.
3.2 x 1013 is correct scientific notation
23.6 x 10-8 is not correct scientific
notation
Remember that the
first number MUST
BE greater than or
equal to one and
less than 10.
4
Converting to Scientific Notation...
To change from Standard Form to Scientific Notation:
1) Place the decimal so that there is one non-zero digit
to the left of the decimal point.
2) Count the number of decimal places the decimal has
"moved" from the original number. You will use this
for the exponent of 10.
3) If the original number was less than 1, the exponent
will be negative; if the original number was greater
than 1, the exponent will be positive.
EXAMPLES:
a. 5,230,000
The original number
was greater than 1 so
the exponent is positive.
b. 0.000695
The original number
was less than 1 so the
exponent is negative.
5
Converting from Scientific Notation...
To change from Scientific Notation to Standard Form:
1) Move the decimal to the right for positive exponents
of 10. The exponent will tell you how many places to
move.
2) Move the decimal to the left for negative exponents
of 10. The exponent will tell you how many places to
move.
EXAMPLES:
a. 2.135 x 10-8
Negative exponents
move the decimal to
the left.
b. 6.193 x 103
Positive exponents
move the decimal to
the right.
6
Try these:
Express the following in correct scientific notation.
1. 42,000
2. 1,349,000
3. 732
4. 6,200
5. 0.0000568
6. 0.07085
7
Try these:
Express the following in correct standard form.
7. 1.03 x 107
8. 6.2283 x 108
9. 7.038 x 10-4
10. 6.002 x 10-2
11. 4.8 x 105
12. 8.9321 x 104
8
To Multiply:
To multiply 2 numbers expressed in scientific notation,
simply multiply the numbers out front and add the
exponents.
If you wanted to think of it in terms of a formula:
EXAMPLES:
a.
b.
9
To Divide:
To divide 2 numbers expressed in scientific notation,
simply divide the numbers out front and subtract the
exponents.
If you wanted to think of it in terms of a formula:
EXAMPLES:
a.
b.
c.
10
Try these:
Multiply or divide the following. Be sure your final
answers are in scientific notation.
1.
2.
3.
4.
11
What if I have to add or subtract numbers in scientific
notation?
You can always convert to standard form and add
or subtract like normal.
12
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Attachments
Revised_8_Math_Unit_2_Powers_That_Be_SE_09309.pdf