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Technical Science
Scientific Tools and Methods
Scientific Notation
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.
Purpose of Scientific Notation Very often scientists are forced to work with
very large or very small numbers.
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The sun is 93 million miles from earth.– 93,000,000 miles
Bacterial cells measure about 1 micrometer.– 1 um = 0.000001 meters
A computer has a 10 gigabyte hard drive.– 10 Gb = 10,000,000,000 bytes
Purpose of Scientific Notation There are some problems with these very
large and very small numbers.
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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.
93,000,000 mi 0.000001 m 10,000,000,000 bytes
Purpose of Scientific Notation Scientific notation was developed to solve
the problem of writing very large and small numbers.
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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
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.
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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.
93,000,000 = 9.3 x 107
Stem
Purpose of Scientific Notation? Which number below is written in scientific
notation?
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A 1.82 x 10 -6 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.
– 1.82 x 10-6
– 18.2 x 106
– 0.182 x 106
Purpose of Scientific Notation The power of ten has two parts. There is a
base and there is an exponent
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The base will always be 10. The exponent in this example is 7.
93,000,000 = 9.3 x 107
Base = 10
Exponent = 7
Purpose of Scientific Notation The power of ten part is a short way of
writing all the zeros.
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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
93,000,000 = 9.3 x 107
Purpose of Scientific Notation Let’s put it all together and see how
scientific notation works.
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9.3 x 107 = 93,000,000
9.3 x 10,000,000 = 93,000,000
6.83 x 103 = 6,830
6.83 x 1,000 = 6,830
Purpose of Scientific Notation
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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.
The “power of ten” part of a number in scientific notation is a multiple of 10.
93,000,000 = 9.3 x 107
107 = 10,000,0009 3,000,000.
7 places
9.3 x 10 7
Purpose of Scientific Notation? Which number below is written in scientific
notation?
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A 8.5 x 10 4 is the only number that is written strictly in scientific notation because the base must be 10.
– 1.82 x 610
– 8.5 x 104
– 3.1 x 1006
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Convert Standard Formto Scientific Notation Writing a number in scientific notation is a
three step process.
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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.
Convert Standard Formto Scientific Notation ? Write 8,760,000,000 in scientific notation.
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Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.
8 7 6 0 0 0 0 0 0 0 ..
8.76 is the Stem
Convert Standard Formto Scientific Notation ? Write 8,760,000,000 in scientific notation.
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Step 2: The number of places you moved the decimal will be the exponent on the power of 10
8 7 6 0 0 0 0 0 0 0 ..
8.76 is the Stem
9 places
10 9 is the Power of 10
Convert Standard Formto Scientific Notation ? Write 8,760,000,000 in scientific notation.
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Step 3: Write the number so it is the stem times the power of ten.
8 7 6 0 0 0 0 0 0 0 ..
8.76 is the Stem9 places
10 9 is the Power of 10
8.76 x 10 9 = 8,760,000,000
Convert Standard Formto Scientific Notation ? Write the following numbers in scientific
notation.
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660,000,000 =
90300 =
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
8.0001 x 109
1.594 x 105
7.3 x 103
Convert Standard Formto Scientific Notation There are two differences when writing a
small number in scientific notation.
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First, the decimal will be moved in the opposite direction.
Second, the exponent will be written as a negative number.
Convert Standard Formto Scientific Notation ? Write 0.00000000482 in scientific notation.
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Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.
0 0 0 0 0 0 0 0 0 4 8 2. .
4.82 is the Stem
Convert Standard Formto Scientific Notation ? Write 0.00000000482 in scientific notation.
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0 0 0 0 0 0 0 0 0 4 8 2. .
4.82 is the Stem
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
10 -9 is the Power of 10
Convert Standard Formto Scientific Notation ? Write 0.00000000482 in scientific notation.
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0 0 0 0 0 0 0 0 0 4 8 2. .
4.82 is the Stem
Step 3: Write the number so it is the stem times the power of ten.
9 places
10 -9 is the Power of 10
4.82 x 10 -9 = 0.00000000482
Convert Standard Formto Scientific Notation ? Write the following numbers in scientific
notation.
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0.00543 =
0.00000074 =
0.03397 =
0.00006008 =
0.00000000081 =
0.000105 =
0.0000073 =
5.43 x 10 -3
7.4 x 10 -7
3.397 x 10 -2
6.008 x 10 -5
8.1 x 10 -10
1.05 x 10 -4
7.3 x 10 -6
Convert Scientific Notationto Standard Form Converting scientific notation to a number
in standard form is the same process in reverse.
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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
Convert Scientific Notationto Standard Form ? Write 1.98 x 109 in standard form.
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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.
1 9 8 x 10 9. 0 0 0 0 0 0 0.
1.98 x 109 = 1,980,000,000
9 places
? Write the following numbers in standard form.
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2.9 x 104 =
6.87 x 106 =
1.008 x 109 =
3.04 x 105 =
8.8 x 1010 =
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
Convert Scientific Notationto Standard Form
Convert Scientific Notationto Standard Form ? Write 5.37 x 10-9 in standard form.
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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.
5 3 7 x 10 -9.0 0 0 0 0 0 0 0 0.
5.37 x 10-9 = 0.00000000537
9 places
? Write the following numbers in standard form.
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2.9 x 10-4 =
6.87 x 10-6 =
1.008 x 10-9 =
3.04 x 10-5 =
8.8 x 10-10 =
7.52 x 10-2 =
5.73 x 10-7 =
0.00029
0.00000687
0.000000001008
0.0000304
0.00000000088
0.0752
0.000000573
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Scientific Notation