GGG SN
Name:
SCIENTIFIC NOTATION ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Scientific notation is a special way of writing numbers that are really big (like
2,450,000,000) or really small (like 0.00000003698).
❊ Look at this BIG number written in standard form: 5,230,000,000
Here’s the same number written in scientific notation: 5.23 x 109
❊ Look at this SMALL number written in standard form: 0.0000079
Here’s the same number written in scientific notation: 7.9 x 10-6
Scientific notation always looks like this:
______ x 10☐
Multiplied by a
power of 10
A number bigger than
1 but less than 10
The exponent on the 10 is…
• POSITIVE when the number is big.
• NEGATIVE when the number is small.
(The exponent on the 10 tells the number of places that the decimal point has been
moved.)
EXAMPLES (Standard Form  Scientific Notation)
934,000,000
9.34 x 108
The decimal point is currently at the end of the number, after
the last zero. For scientific notation, it needs to end up
between the 9 and the 3. It needs to be moved 8 places to end
up there.
934,000,000 is a BIG number, so the 8 will be positive.
0.00000000045
4.5 x 10-10
The decimal point is currently at the beginning of the number.
For scientific notation, it needs to end up between the 4 and
the 5. It needs to be moved 10 places to end up there.
0.00000000045 is a SMALL number, so the 10 will be negative.
Algebra 1
PRACTICE: Scientific Notation
Name
Write each number in scientific notation.
1.
0.0000006
6.
2,000,000
2.
5,400,000
7.
48,900
3.
60
8.
0.0000009
4.
0.009
9.
0.000216
5.
0.0000067
10.
6,829,300
Write each number in standard notation.
11. 3.24 ⋅107
16. 3 ⋅10−6
12. 4.5⋅105
17. 9.182 ⋅109
13. 9.834 ⋅10−4
18. 1.665⋅10−3
14. 7.9 ⋅10−8
19. 7 ⋅10−5
15. 9 ⋅104
20. 8.54 ⋅1011
Algebra 1
SCIENTIFIC NOTATION PRACTICE
Name
Some examples…
Standard Form
Scientific Notation
1,500
1.5 x 103
20,000,000
2.0 x 107
427,300,000
99,000,000,000,000,000
0.00000008
4.273 x 108
9.9 x 1016
8.0 x 10-8
0.000036
3.6 x 10-5
Convert the numbers below into scientific notation. Include the units!
1. The richest man in the world is William Henry Gates III whose net worth
is $40,000,000,000.
2. The most downloaded song in 2011 was “Rolling in the Deep” performed
by Adele (over 5,800,000 downloads).
3. The average distance from the Earth to the Moon is
250,000 miles.
4. The distance around the world (Earth’s circumference) is 24,900 miles.
5. The diameter of an atom is about 0.0000000001 meters.
6. The fastest land speed record is 763 mph.
Convert the numbers below into standard form. Include the units!
7. Earth is about 9.3 x 107 miles from the sun.
8. The diameter of a red blood cell is about 6.5 x 10-3 meters.
9. The mass of a water molecule is 2.99 x 10-23 grams.
10. Earth’s diameter is 7.92641 x 103 miles, Jupiter’s diameter is 8.887 x 104 miles, and
Venus’s diameter is 7.518591 x 103 miles.
Which planet has the largest diameter?
Which has the smallest?
11. Use the table below to answer each question.
United States
China
Population
3.1159191 x 108
1.338299 x 109
Land Area (km2)
9.8266 x 106
9.598 x 106
Population of the Most
Populous City
New York
8.1751 x 106
Shanghai
2.2315 x 107
a. Which country has the larger population?
b. Rewrite the land area of the United States in standard form.
c. Rewrite the population of Shanghai in standard form.
d. The population of India is 1,170,839,000. How does this population compare to
that of the United States and China?