Wize University Statics Textbook (Master) > Introduction

Scientific Notation

Instead of writing very large or very small number we can express these numbers as a number between -10 and positive 10 (exclusively) multiplied by 10n
Write the following in scientific notation
584= 

4 529 000=

78 000 000=

0.00000128=

584=5.84×102584=5.84\times10^2584=5.84×102
4,529,000=4.529×1064,529,000=4.529\times10^64,529,000=4.529×106
78,000,000=7.8×10778,000,000=7.8\times10^778,000,000=7.8×107
0.00000128=1.28×10−60.00000128=1.28\times10^{-6} 0.00000128=1.28×10−6

Scientific Notation in Calculations
You want to make the values you are adding or subtracting have the same exponent 

Example: 
7.0x107-6.0x105
We can either change both exponents to 7 or to 5 

For multiplying #s in scientific notation, we add exponents and multiply the #s: (ans in scientific notation)

Example: 
3.0x108 x 4.0x106

Finally, to divide #s in scientific notation, we subtract exponents and divide the #s: (ans in scientific notation)

Example: 
1.2x1012 / 6x106

On average Americans consume about 3.2 hamburgers a week.  If we assume that there are about 52 weeks in a year, and that there are about 300 million Americans, how many hamburgers are consumed in a year?  (Express your answer in scientific notation, rounded to two decimal places).

ANSWER:  We can begin by multiplying the numbers together.

(3.2)(52)(300,000,000)
    = 49920000000 
   = 4.992×1010
   ≈4.99×1010

This is approximately 50 billion hamburgers.  

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Calculate the following, leaving answer in scientific notation.
a)  2.2x106 x 4.1x10-2
b)  2.2x106 / 4.1x10-2

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