Simplify the following Write all the answers using positive exponents. 1) 4 0 = 1 2) – 7w 0 = – 7 3) 4) 5)

12.05 Scientific Notation

Scientific Notation Form Scientific Notation is used to write very large and very small numbers. Numbers like: 93,000,000 0.000025 Scientific Notation Form where a > 1 and a < 10 and n is an integer

a × 10 n Scientific Notation Form To write an number in scientific notation form, move the decimal point until a number between 1 and 10 is reach. This is the “a” value. To find the “n” value. Count the number of decimal places moved. “n” is positive if the decimal was moved to the left. “n” is negative if the decimal was moved to the right.

a × 10 n Scientific Notation Form S.N. 9.3 × 10 7 2.5 × 10 – 5 Write the following numbers in S.N. 93,000,000 There’s no decimal point, place one at the end. 93,000,000.0 Move the decimal point between the 9 and 3 and count the number of decimal places moved. 9.3 × 10 7 0.000025 Move the decimal point between the 2 and 5 and count the number of decimal places moved. 2.5 × 10 – 5

To write a S.N. number without the exponents, move the decimal point “n” places. Move the decimal to the left if “n” is negative. Move the decimal to the right if “n” is positive. 1.86 × 10 5 = 186,000 Move the decimal 5 places to the right. 8.2 × 10 – 7 = 0.00000082 Move the decimal 7 places to the left. 4 × 10 3 = 4,000 9 × 10 – 5 = 0.00009

To find the product or quotient of numbers written in S.N., find the product or quotient of the “ a ” terms and of the “ 10 n “ terms. ( 2 × 10 3 )( 3 × 10 5 ) = ( 2 · 3 ) × ( 10 3 · 10 5 ) = 6 × 10 8 ( 8 × 10 – 2 )( 4 × 10 9 ) = ( 8 · 4 ) × ( 10 – 2 · 10 9 ) = 32 × 10 7 = 3.2 × 10 8 6 × 10 8 6 10 8 _______ ___ ____ × = 3 × 10 5 = 2 × 10 3 2 10 3 10 2 2 × 10 2 2 ________ ___ ____ = × = 0.4 × 10 9 = 4 × 10 8 5 × 10 – 7 5 10 – 7

Try This: Write the following in Scientific Notation 25000 = 2.5 × 10 4 Write the following without Scientific Notation 8 × 10 – 5 = 0.00008 Simplify ( 3 × 10 2 )( 6 × 10 – 8 ) = 18 × 10 – 6 = 1.8 × 10 – 5 9 × 10 7 ________ = 4.5 × 10 1 2 × 10 6