•
•
•
To write in scientific notation numbers far from zero.
To rewrite in standard notation numbers that are in
scientific notation.
To learn how calculators represent scientific notation.
• Did you know that there are approximately
75,000 genes in each human cell and more than
50 trillion cells in the human body?
• This means there are about
75,000▪50,000,000,000,000 or
3,750,000,000,000,000,000 genes in a body.
• We can rewrite each of the number in scientific
notation:
▫ 3,750,000,000,000,000,000 = 3.75 x 1018
A Scientific Quandary
In Scientific Notation
Not in Scientific Notation
3.4 x 105
27 x 104
7.04 x 103
120,000,000
6.023 x 1017
42.682 x 1029
8 x 101
4.23 x 126
1.6 x 102
42 x 102
Classify each of these numbers as in scientific notation or not. If a
number is not in scientific notation, tell why not.
4.7 x 103
32 x 105
1.107 x 1013
0.28 x 1011
24 x 106
A Scientific Quandary
In Scientific Notation
Not in Scientific Notation
3.4 x 105
27 x 104
7.04 x 103
120,000,000
6.023 x 1017
42.682 x 1029
8 x 101
4.23 x 126
1.6 x 102
42 x 102
Define what it means for a number to be in scientific notation.
A Scientific Quandary
• Complete steps 3-5.
▫ Place your calculator in scientific
notation mode.
▫ Enter the number 5000 on the
home screen and press enter.
Your calculator displays the
number in its form of scientific
notation.
• Repeat with each number in
step 5. Record your answers in
a chart.
▫
▫
▫
▫
▫
▫
250,
-5,530
14,000
7,000,000
18
470,000
• Step 6
▫ In scientific notation, how is
the exponent on the 10
related to the number in
standard notation?
▫ How are the digits before
the 10 related to the
number in standard
notation?
▫ If a number in standard
notation is negative, how
does that show up in
scientific notation?
Original
Scientific
250
2.5 x 102
-5,530
-5.53 x 103
14,000
1.4 x 104
7,000,000
7.0 x 106
18
1.8 x 101
-470,000
-4.7 x 105
• Step 7
▫ Write a set of instructions for converting
415,000,000 from standard notation to
scientific notation.
• Step 8
▫ Write a set of instruction for converting
6.4 x 105 from scientific notation to
standard notation.
Example
• Meredith is doing a report on stars and wants
an estimate for the total number of stars in
the universe.
• She reads that astronomers estimate that
there are at least 125 billion galaxies in the
universe.
• An encyclopedia says that the Milky way,
Earth’s galaxy, is estimated to contain more
than 10 billion stars.
• Estimate the total number of stars in the
universe. Give you answer in scientific
notation.
• 125 billion = 1.25 x 1011
• 10 billion = 1.0 x 1010
• (1.25 x 1011)(1.0 x 1010)
=(1.25 x 1) x (1011 x 1010)=1.25 x 1021