1. Technical Science Scientific Tools and Methods
Scientific Notation

2. Scientific Notation In this section you will …
Describe the purpose of Scientific Notation
Convert numbers in standard form to scientific notation
Convert numbers in scientific notation to standard form.

3. Purpose of Scientific Notation
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Very often scientists are forced to work with very large or very small numbers.
The sun is 93 million miles from earth.
93,000,000 miles
Bacterial cells measure about 1 micrometer.
1 um = meters
A computer has a 10 gigabyte hard drive.
10 Gb = 10,000,000,000 bytes

4. Purpose of Scientific Notation
There are some problems with these very large and very small numbers.
93,000,000 mi m
10,000,000,000 bytes
It’s easy to accidentally forget a zero or add an extra one.
Calculating with these numbers is also difficult. Some have too many digits to be entered on a calculator.

5. Purpose of Scientific Notation
Scientific notation was developed to solve the problem of writing very large and small numbers.
Numbers written in scientific notation have two parts: a stem, which is a number between 1 & 10, and a power of 10.
93,000,000 = 9.3 x 107
Stem
Power of 10

6. Purpose of Scientific Notation
Let’s take a closer look at the parts of a number written in scientific notation to see how it works.
93,000,000 = 9.3 x 107
Stem
The stem is always a number between 1 and 10. In this example, 9.3 is the stem and it is between 1 and 10.

7. Purpose of Scientific Notation
Which number below is written in scientific notation?
1.82 x 10-6
18.2 x 106
0.182 x 106
1.82 x is the only number that is written strictly in scientific notation because it is the only one with a stem that is between 1 and 10.

8. Purpose of Scientific Notation
The power of ten has two parts. There is a base and there is an exponent
Exponent = 7
93,000,000 = 9.3 x 107
Base = 10
The base will always be 10.
The exponent in this example is 7.

9. Purpose of Scientific Notation
The power of ten part is a short way of writing all the zeros.
93,000,000 = 9.3 x 107
107 means 10 multiplied by itself 7 times.
10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000
Here are some other examples.
103 = 10 x 10 x 10 = 1000
102 = 10 x 10 = 100

10. Purpose of Scientific Notation
Let’s put it all together and see how scientific notation works.
x = 93,000,000
9.3 x
10,000,000 =
93,000,000
x = 6,830
6.83 x
1,000 =
6,830

11. Purpose of Scientific Notation
The “power of ten” part of a number in scientific notation is a multiple of 10.
107 = 10,000,000
93,000,000 = 9.3 x 107
9.3 x 10 7
9 3,000,000.
7 places
Multiplying by a multiple of ten can be done by moving the decimal.
The exponent on the “power of ten” tells how many places to move the decimal.

12. Purpose of Scientific Notation
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Which number below is written in scientific notation?
1.82 x 610
8.5 x 104
3.1 x 1006
8.5 x 10 4 is the only number that is written strictly in scientific notation because the base must be 10.

13. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
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Writing a number in scientific notation is a three step process.
We will start by writing large numbers in scientific notation then we will write small numbers in scientific notation.
You will see a step by step example and then you will have a chance to practice.

14. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . .
8.76 is the Stem

15. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 2: The number of places you moved the decimal will be the exponent on the power of 10 . .
9 places
8.76 is the Stem
10 9 is the Power of 10

16. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 3: Write the number so it is the stem times the power of ten. . .
9 places
8.76 is the Stem
10 9 is the Power of 10
8.76 x = 8,760,000,000

17. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write the following numbers in scientific notation.
660,000,000 = =
397 =
4,500,000 =
8,000,100,000 =
159,400 =
7,300 =
6.6 x 108
9.03 x 104
3.97 x 102
4.5 x 106
x 109
x 105
7.3 x 103

18. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
There are two differences when writing a small number in scientific notation.
First, the decimal will be moved in the opposite direction.
Second, the exponent will be written as a negative number.

19. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . .
4.82 is the Stem

20. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1. . .
9 places
4.82 is the Stem
10 -9 is the Power of 10

21. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 3: Write the number so it is the stem times the power of ten. . .
9 places
4.82 is the Stem
10 -9 is the Power of 10
4.82 x =

22. Convert Standard Form to Scientific Notation
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Convert Standard Form to Scientific Notation
Write the following numbers in scientific notation. = = = = = = =
5.43 x
7.4 x x x
8.1 x
1.05 x
7.3 x

23. Convert Scientific Notation to Standard Form
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Convert Scientific Notation to Standard Form
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Converting scientific notation to a number in standard form is the same process in reverse.
The exponent tells you how many places to move the decimal on the stem.
A positive exponent says the number is bigger than the stem; move the decimal accordingly
A negative exponent says the number is smaller than the stem; move the decimal accordingly

24. Convert Scientific Notation to Standard Form
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Convert Scientific Notation to Standard Form
Write x 109 in standard form.
The exponent tells us to move the decimal 9 places.
A positive exponent means the number is bigger than the stem. To make 1.98 bigger, we must move the decimal to the right. .
x 10 9 .
9 places
1.98 x 109 = 1,980,000,000

25. Convert Scientific Notation to Standard Form
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Write the following numbers in standard form.
2.9 x 104 =
6.87 x 106 =
1.008 x 109 =
3.04 x 105 =
8.8 x =
7.52 x 102 =
5.73 x 107 =
29,000
6,870,000
1,008,000,000
304,000
88,000,000,000
752
57,300,000

26. Convert Scientific Notation to Standard Form
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Convert Scientific Notation to Standard Form
Write x in standard form.
The exponent tells us to move the decimal 9 places.
A negative exponent means the number is smaller than the stem. To make 5.37 smaller, we must move the decimal to the left. . x .
9 places
5.37 x =

27. Convert Scientific Notation to Standard Form
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Write the following numbers in standard form.
2.9 x =
6.87 x =
1.008 x =
3.04 x =
8.8 x =
7.52 x =
5.73 x =
0.0752

28. Technical Science Scientific Tools and Methods
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Scientific Notation