6.1.3 – Scientific Notation

Recall, an exponent is another way to express a large or small number in a smaller form One particular application has to do with very large, or very small numbers from science or similar that often are too cumbersome to write out

Scientific Notation = number written in the form c x 10 n, where 1 ≤ c < 10, and n is an integer (not a decimal or fraction) What is the base? What represents the exponent?

We can multiply and divide numbers in scientific notation much the same way we multiply and divide our other exponents Multiplication; multiply coefficients (c values), add exponents Division; divide coefficients (c values), subtract exponents Final answers should also be in scientific notation; may have to change power or decimal if c ≥ 10 or c < 1

Example. Simplify (4 x ) (9 x ) What is ending coefficient? Is it in scientific notation?

Example. Simplify (4.7 x 10 9 ) x (2 x 10 4 )

Example. Simplify (6 x 10 5 )/(2 x 10 4 )

Example. Simplify (5.5 x )/(11 x )

Per Capita In economics, science, and sociology, often times we may try to determine the amount of items used per person, or similar Per Capita = amount for each person (per person) Many examples could be made; what are some we could come up with?

Example. In 2003, approximately 4.25 x phone calls were made in the United States. The population during that time was about 2.91 x 10 8 individuals. Find the per capita of phones per US resident.

Example. In 2012, the total money made by the US for GDP (gross domestic product, or products produced in the US) was x The population for 2012 in the US was approximately x Find the per capita GDP.

Assignment Pg. 299, 36-39, 46-50