9-5 Scientific Notation
Express each number in standard form.
10. 6.89 × 104
SOLUTION: 11. 1.5 × 10−4
SOLUTION: 12. 2.3 × 10−5
SOLUTION: 13. 9.51 × 10−3
SOLUTION: 14. 3.062 × 106
SOLUTION: 15. 7.924 × 102
SOLUTION: 16. MONEY A dollar bill is approximately 1.09 × 10−2 centimeter thick.
SOLUTION: 17. E-MAILS It is estimated that more than 1.71 × 102 billion e-mails are sent each day around the world. Most of
these are spam and viruses.
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16. MONEY A dollar bill is approximately 1.09 × 10
centimeter thick.
SOLUTION: 9-5 Scientific Notation
17. E-MAILS It is estimated that more than 1.71 × 102 billion e-mails are sent each day around the world. Most of
these are spam and viruses.
SOLUTION: Express each number in scientific notation.
18. 700,000
SOLUTION: 19. 32,000,000
SOLUTION: 20. 0.045
SOLUTION: 21. 0.000918
SOLUTION: 22. 1,000,000
SOLUTION: 23. 0.006752
SOLUTION: 24. WEATHER Each minute, there are approximately 6 × 103 flashes of lightning around the world. The air around a
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lightning bolt is heated to about 5.4 × 10 degrees Fahrenheit, which is about five times hotter than the Sun.
a. About how many flashes of lightning are there in a day? Write in scientific notation and in standard form.
b. About how hot is the Sun in degrees Fahrenheit? Write in scientific notation and in standard form.
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SOLUTION: a. To find how many flashes of lightening there are in a day, multiply the number of flashes per minute by the
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23. 0.006752
SOLUTION: 9-5 Scientific Notation
24. WEATHER Each minute, there are approximately 6 × 103 flashes of lightning around the world. The air around a
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lightning bolt is heated to about 5.4 × 10 degrees Fahrenheit, which is about five times hotter than the Sun.
a. About how many flashes of lightning are there in a day? Write in scientific notation and in standard form.
b. About how hot is the Sun in degrees Fahrenheit? Write in scientific notation and in standard form.
SOLUTION: a. To find how many flashes of lightening there are in a day, multiply the number of flashes per minute by the
number of minutes in a day. There are 60 minutes in one hour and 24 hours in one day. So, there are 60 × 24 or 1440
minutes in one day.
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So, there are about 8.64 × 10 , or 8,640,000, flashes of lightning in day.
b. To find the temperature of the Sun, divide the temperature of the air around a lightning bolt by 5.
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So, the Sun is about 1.08 × 10 , or 10,800, degrees Fahrenheit.
Order each set of numbers from least to greatest.
25. 2.4 × 102, 2.45 × 10−2, 2.45 × 102, 2.4 × 10−2
SOLUTION: Because two of the numbers have an exponent of −2, compare their factors.
2.4 < 2.45
−2
−2
So, 2.4 × 10 is less than 2.45 × 10 .
Because the other two numbers have an exponent of 2, compare their factors.
2.4 < 2.45
2
2
So, 2.4 × 10 is less than 2.45 × 10 .
2
2
−2
−2
The numbers in order from least to greatest are 2.4 × 10 , 2.45 × 10 , 2.4 × 10 , 2.45 × 10 .
26. 2.81 × 104, 2805, 2.08 × 105, 3.2 × 104, 3.024 × 102
SOLUTION: 3
2805 written in scientific notation is 2.805 × 10 . Only two of the numbers have the same exponent of 4. Compare
their factors.
2.81 < 3.2
4
4
So, 2.81 × 10 is less than 3.2 × 10 .
The rest of the numbers can be ordered using their exponents.
2
4
4
5
The numbers in order from least to greatest are 3.024 × 10 , 2805, 2.81 × 10 , 3.2 × 10 , 2.08 × 10 .
27. 5.9 × 106, 5.9 × 104, 5.01 × 105, 5.1 × 10−3
SOLUTION: Because the exponents are different, they can be used to order the numbers.
−3 < 4 < 5 < 6
4
5
6
−3
The numbers in order from least to greatest are 5.1 × 10
, 5.9 × 10 , 5.01 × 10 , 5.9 × 10 .
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28. 9,562,301, 9.05 × 10−6, 9.5 × 106, 905,000
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2.81 < 3.2
4
9-5
4
So, 2.81 × 10 is less than 3.2 × 10 .
The rest of the numbers can be ordered using their exponents.
Scientific Notation
2
4
4
5
The numbers in order from least to greatest are 3.024 × 10 , 2805, 2.81 × 10 , 3.2 × 10 , 2.08 × 10 .
27. 5.9 × 106, 5.9 × 104, 5.01 × 105, 5.1 × 10−3
SOLUTION: Because the exponents are different, they can be used to order the numbers.
−3 < 4 < 5 < 6
4
5
6
−3
The numbers in order from least to greatest are 5.1 × 10 , 5.9 × 10 , 5.01 × 10 , 5.9 × 10 .
28. 9,562,301, 9.05 × 10−6, 9.5 × 106, 905,000
SOLUTION: 6
5
9,562,301 written in scientific notation is 9.562301 × 10 . 905,000 written in scientific notation is 9.05 × 10 . Only
two of the numbers have the same exponent of 6. Compare their factors.
9.5 < 9.562301
6
So, 9.5 × 10 is less than 9,562,301.
The rest of the numbers can be ordered using their exponents.
6
−6
The numbers in order from least to greatest are 9.05 × 10 , 905,000, 9.5 × 10 , 9,562,301.
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