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 10n, 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 1012) (9 x 10-3)• What is ending coefficient? Is it in scientific notation?

• Example. Simplify (4.7 x 109) x (2 x 104)

• Example. Simplify (6 x 105)/(2 x 104)

• Example. Simplify (5.5 x 10-5)/(11 x 1012)

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 1011 phone calls were made in the United States. The population during that time was about 2.91 x 108 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 1.624 x 1014. The population for 2012 in the US was approximately 3.139 x 109. Find the per capita GDP.

• Assignment• Pg. 299, 36-39, 46-50