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Scientific Notation By Jenny Erickson

What is scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10x

Which of these are in scientific notation? What are the common equivalents? 1.0 X 100 10.2 X 102 0.1 100 1.5 x 101

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Example 1 Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 2 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

Changing scientific notation to standard form.

To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

Example 3 Given: 5.093 x 106 Answer: 5,093,000 (moved 6 places to the right)

Example 4 Given: 1.976 x 10-4 Answer: 0.0001976 (moved 4 places to the left)

How do I convert these to scientific notation? 0.123456789 123456789 1,000,000,000,000,000,000 0.000000000123456789 ( 0.000 000 000 123456789)

Multiplying and Dividing

Multiplying in Scientific Notation

Multiplying… The general format for multiplying is as follows… (N x 10x)(M x 10y) = (N)(M) x 10x+y First multiply the N and M numbers together and express an answer. Secondly multiply the exponential parts together by adding the exponents together. Finally multiply the two results for the final answer.

Multiplying… 7.45 x 106 (2.41 x 104)(3.09 x 102) 2.41 x 3.09 = 7.45 4 + 2 = 6 7.45 x 106

Dividing in Scientific Notation

Dividing… The general format for dividing is as follows… (N x 10x)/(M x 10y) = (N/M) x 10x-y First divide the N number by the M number and express as an answer. Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number. Finally multiply the two results together to get the final answer.

Dividing… (4.89 x 107)/(2.74 x 104) 4.89 / 2.74 = 1.78 7 – 4 = 3 1.78 x 103

Even More Practice Below is a list of links to games and activities all having to do with scientific notation. http://www.aaamath.com/dec71i-dec2sci.html http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl http://www.sciencejoywagon.com/physicszone/lesson/00genral/dectosci.htm

Now take the quiz to test your scientific notation skills! Click on the link below to take the quiz and then use the answer key for the correct answers. Quiz Answers

Quiz Time!!! Below is a set of links for a quiz on multiplying and dividing numbers in scientific notation, and there is a link to get the answers to the quiz. Quiz on Multiplying and Dividing Answers to Quiz