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Wize University Physics Textbook (Master) > Foundations / Introduction / Measurement

Scientific Notation

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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\times10^2
4,529,000=4.529×1064,529,000=4.529\times10^6
78,000,000=7.8×10778,000,000=7.8\times10^7
0.00000128=1.28×10−60.00000128=1.28\times10^{-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