MA.8.A.6.1 Use exponents and scientific notation to write large & small numbers and vice versa & to solve
problems.
DEFINITIONS
Exponential Form: The number of times the base occurs as a factor. The number 2, is the base, and the number 3 is
called the exponent.
Ex. 23 = 2 x 2 x 2
Scientific Notation: a method of writing very large or very small numbers using exponents in which a number is
expressed as the product of the power of 10 and number that is greater then or equal to (1) and less then 10.
Ex. 7.59 x 105 = 759,000
Standard Form:
EXAMPLES
Example 1 Write 8.65 × 107 in standard form.
8.65 × 107 = 8.65 × 10,000,000
=
107 = 10 · 10 · 10 · 10 · 10 · 10 · 10 or 10,000,000
The decimal point moves 7 places to the right.
Example 2 Write 9.2 × 10-3 in standard form.
9.2 × 10-3 = 9.2 × 0.001
The decimal point moves 3 places to the left.
=
Example 3 Write 76,250 in scientific notation.
= 7.625 × 10,000
= 7.625 × 104
The decimal point moves 4 places.
Since 76,250 is >1, the exponent is positive.
Example 4 Write 0.00157 in scientific notation.
= 1.57 × 0.001
= 1.57 × 10-3
The decimal point moves 3 places.
Since 0.00157 is <1, the exponent is negative.
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Computing with Scientific Notation
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MA.8.A.6.1 Practice Problems
1. The diameter of Jupiter at its equator is approximately
143,000,000 meters. What is 143,000,000 written in
scientific notation?
A. 1.43 × 10-3
B. 1.43 × 106
C. 1.43 × 108
D. 1.43 × 109
2. Red tide is a high concentration of algae that can be
harmful to marine animals and humans. Along the gulf
coast of Florida, red tide is typically caused by the
organism Karenia brevis. These organisms can be as
large as 4.5 × 10-5 meters. What is 4.5 × 10-5 written in
standard form?
A. 4,500,000
B. 450,000
C. 0.000045
D. 0.0000045
3. The John F. Kennedy Space Center, was the site of the
first space shuttle launch. Launching a shuttle requires
more than one million pounds of solid propellant and
5 × 105 gallons of super-cold liquid oxygen and liquid
hydrogen. What is 5 × 105 in standard form?
A. 500,000
B. 100,000
C. 3,125
D. 250
5. The Earth has a diameter of about 1.27 × 104 kilometers.
The dwarf planet Pluto’s diameter is estimated to be about
2.3 × 103 kilometers. About how many times larger is the
diameter of Earth compared to Pluto?
A. 0. 5
B. 2
C. 5
D. 10
4. What is the number 0.0004207 written in scientific
notation?
A. 4.207 × 104
B. 4.207 × 10-3
C. 4.207 × 10-4
D. 4.207 × 10-6
6. The table lists the populations of five countries. List the
countries from least to greatest population.
7. A CD can store about 650,000,000 bytes of data. Write
this number in scientific notation.
Country
Population
South Africa
2.0 x 107
England
1.9 x 108
Japan
7.7 x 107
Spain
4.7 x 105
Germany
4.4 x 106
8. The diameter of the Sun is about 1.39 × 109 meters.
Write this number in standard notation.
9. The table shows the amount of money raised by each
region for cancer awareness. How much money did the
North and South raise together?
10. In one week a small library checked out 1.2 x 10³
books. This is 1/5 the total number of books in the library.
How many books does the library have all together?
Region
North
South
East
West
Amount Raised
1.46 x 104
2.38 x 104
6.75 x 103
8.65 x 103
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11.
12.
13.
14.
By studying lunar samples, scientists have learned the Moon
is approximately 4,600,000,000 years old. What is this
number expressed in scientific notation?
15.
16. Solve
17. Solve
-4
-8
5.16 x 10 ÷ 8.65 x 10 + 9.68 x 10
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The speed of light is about 1.86 × 105 miles per second.
Write this number in standard notation.
2.775 x 10-4 – 4.775 x 104
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4
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21.
5
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