8.9: Scientific Notation with a Calculator
What if you knew that a milligram was onemillionth of a kilogram? How could you express this relationship exponentially? After completing this Concept, you'll be able to solve realworld problems like this one that involve scientific notation.
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Foundation: 02809S Applications Using Scientific Notation
Guidance
Let's look at some realworld applications involving scientific notation.
Example A
The mass of a single lithium atom is approximately one percent of one millionth of one billionth of one billionth of one kilogram. Express this mass in scientific notation.
Solution
We know that a percent is
Next we use the product of powers rule we learned earlier:
The mass of one lithium atom is approximately
Example B
You could fit about 3 million
Solution
Since we need our answer in scientific notation, it makes sense to convert 3 million to that format first:
Next we need an expression involving our unknown, the area taken up by one bacterium. Call this
Isolate
The area of one bacterium is
(Notice that we had to move the decimal point over one place to the right, subtracting 1 from the exponent on the 10.)
Evaluate Expressions in Scientific Notation Using a Graphing Calculator
All scientific and graphing calculators can use scientific notation, and it’s very useful to know how.
To insert a number in scientific notation, use the [EE] button. This is [2nd] [,] on some TI models.
For example, to enter
(To change the mode, press the ‘Mode’ key.)
Example C
Evaluate
Solution
Enter 2.3 [EE]
The calculator displays 6.296296296E16 whether it’s in Normal mode or Scientific mode. That’s because the number is so big that even in Normal mode it won’t fit on the screen. The answer displayed instead isn’t the precisely correct answer; it’s rounded off to 10 significant figures.
Since it’s a repeating decimal, though, we can write it more efficiently and more precisely as
Watch this video for help with the Examples above.
CK12 Foundation: Applications using Scientific Notation
Vocabulary
 In scientific notation, numbers are always written in the form
a×10b , whereb is an integer anda is between 1 and 10 (that is, it has exactly 1 nonzero digit before the decimal).
Guided Practice
Evaluate
Solution
Enter (4.5 [EE]
The calculator displays 9.1125E43. The answer is
Practice
For questions 19, use a calculator to evaluate the expression.

(3.5×104)⋅(2.2×107) 
2.1×1093×102 
(3.1×10−3)⋅(1.2×10−5) 
7.4×10−53.7×10−2 
12,000,000×400,000 
3,000,000×0.00000000022 
17,000680,000,000 
25,000,0000.000000005 
0.00000000000420.00014
 The moon is approximately a sphere with radius
r=1.08×103 miles . Use the formula Surface Area=4πr2 to determine the surface area of the moon, in square miles. Express your answer in scientific notation, rounded to two significant figures.  The charge on one electron is approximately
1.60×1019 coulombs. One Faraday is equal to the total charge on6.02×1023 electrons. What, in coulombs, is the charge on one Faraday?  Proxima Centauri, the next closest star to our Sun, is approximately
2.5×1013 miles away. If light from Proxima Centauri takes3.7×104 hours to reach us from there, calculate the speed of light in miles per hour. Express your answer in scientific notation, rounded to 2 significant figures.
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Here you'll learn how to use a calculator to evaluate scientific notation expressions, and how to work with realworld applications involving scientific notation.