8.4 Use Scientific Notation
Warm-up:
3
5
1. Evaluate:  
2
2. Evaluate: 47  43
18 x3 y 4
4. Simplify:
12 x 2 y 3
4 0
3. Simplify: 6a b
5. A human cell uses on average about 10 12 watts of power. The laser in a CD-R drive
uses about 109 times as many watts. About how many watts of power does the laser in a
CD-R drive use?
6. Order the numbers 0.014, 0.1, 0.01 and 0.11 from least to greatest.
______________________________________________________________________
Goal  Read and write numbers in scientific notation.
VOCABULARY
SCIENTIFIC NOTATION:
A number is written in scientific notation when it is of the form________________________ where
1 ≤ c < 10 and n is an integer.
Scientific
Number
Standard form
notation
Sixteen million
____________
_______________
Two hundredths
____________
_______________
Example 1 Write numbers in scientific notation
a. 7,820,000 = _____•10––
Move decimal point___ places to the___________.
Exponent is______.
Exponent is______.
1
Move decimal point ___ places to the___________.
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b. 0.00401 = _____• 10––
Example 2
Write numbers in standard form
a. 3.89 • 109 = ___________
Exponent is____.
Move decimal point ___ places to the _____________.
b. 9.097 • 10–5 =___________
Exponent is____.
Move decimal point ___ places to the _____________.
Checkpoint Complete the following exercise.
1. Write the number 0.0899 in scientific notation:
2. Write the number 6.0001 • 107 in standard form:
Example 3
Order numbers in scientific notation
Order 3.2 • 10–4, 0.0004, and 2.8 • 10–5 from least to greatest.
Solution
Step 1 Write each number in scientific notation, if necessary.
0.0004 = __________________
Step 2 Order the numbers. First order the numbers with different powers of 10. Then order the
numbers with the same power of 10.
Because 10–5 ____ 10–4, you know that ______________is less than both ______________
and ____________________.
Because 3.2 ___ 4, you know that_______________ is less than_______________.
So, __________________<____________________<___________________.
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2
Step 3 Write the original numbers in order from least to greatest:
Checkpoint Complete the following exercise.
3. Order 225,000,1,740,000, and 1.75 • 105 from least to greatest.
Example 4
Compute with numbers in scientific notation
Evaluate the expression. Write your answer in scientific notation.
a. (5.6 • 10–4)(1.4 • 10–5)
= (5.6  1.4) • (10–4  10–5)
Commutative property and associative property
= ________ • ________
Product of powers Property
b. (3.2 • 102)3
= ________ • ________
= ________ • ________
= (__________) • _______
c.
Power of a product property
Power of a power property
Write _______ in scientific notation.
= ________ • (________)
Associative property
= ____________
Product of powers property
3.5 • 10 –3
1.75 • 10 –5
3.5 10–3
= 1.75 • –5
10
= ____ • ____
Product rule for
fractions
Quotient of powers
Property
Checkpoint Simplify the expression.
6 • 10–4
3
5.
4.8 • 10–4
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4.
(2.01•10–7)2