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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Scientific Notation – Guided Notes – Section 5.11 Scientific Notation is used to write numbers that are very large or very small. For example, the Earth has a mass of about 5,973,700,000,000,000,000,000,000 kg. This can be expressed as ________________________. And the mass of a carbon atom is about 0.000000000000000000000000000166 kg. This can be expressed as ___________________________. How/Why does this work? First consider powers of 10. Example 1: Express each number as a power of 10. a. 100,000 d. −0.000001= −
b. 0.0001=
!
!""""""
!
!""""
e. −1,000,000,000 c.
10,000,000 f.
−0.01= −
!
!""
Then recognize that when you multiply a number by a power of 10, the effect is that you move the decimal point. Example 2: Simplify the following expressions. b. −3.1 x 10! = −3.1 x 10000000 a. 2.45 x 100000 = 2.45 x 10! 7.46 x 10!! = 7.46 x 0.001 c.
d. −9.81 x 10!! = −9.81 x 0.00001 1 Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
This fact about powers of tens allows us to more easily write really big or really small numbers. Definition: A number written in scientific notation has the following form: 𝑎 x 10! or −𝑎 x 10! Where _________ ≤ 𝑎 < ___________. Or in other words, where a is ______________________________________________ one and _______________________________ 10. Example 3: Each of the numbers below is in scientific notation. Write each in standard or decimal notation. a. 3.4 x 10! b. −4.56 x 10! c.
8.88 x 10!! d. −8 x 10!! e. 1.02 x 10!! f.
−7.345 x 10! Example 4: Write each of the numbers below in scientific notation. a. 1,340,000 b. 0.00000609 c.
d. 0.9 x 10! e. −379 x 10! f.
−3 1.3 x 10! 6 x 10! 2 Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Practice: 1. Write each of the following numbers in standard notation. b. −2.89 x 10! a. 3.456 x 10! c.
8.221 x 10!! d. −1.34 x 10!! 2. Write each of the following numbers in scientific notation. a. 0.0000388 b. −0.0074 c.
d. 6,043,000,000 e. 0.234 x 10!! f.
543 x 10! 2.2x 10! 5 x 10! 3
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