Scientific and standard notation, conversion

What is Scientific Notation A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (eg, 7000 = 7 x 103 or 0.0000019 = 1.9 x 10 -6) Why do we use it? It’s a shorthand way of writing very large or very small numbers used in science and math and anywhere we have to work with very large or very small numbers.

Scientific and standard notation, conversion Scientific Notation: expressing a number in the form c x 10n , where 1 < c < 10. Examples: Are the following numbers written in scientific notation? a. 42 x 106 b. 9.3 x 103 No, 42 is Yes greater than 10

Move the decimal left or right so that c is between 1 and 10 Move the decimal left or right so that c is between 1 and 10. Count the # of places you moved. Examples: Write in scientific notation: a. 236,000 b. 0.04325 c. 0.000725 2.36 x 105 4.325 x 10–2 7.25 x 10-4

Example: Write in decimal notation: a. 2.45 x 10–3 b. 1.38 x 108 To change from scientific notation back to decimal notation, move the decimal n of places, where n is the power of 10. 0.00245 138,000,000 Example: Write in decimal notation: a. 2.45 x 10–3 b. 1.38 x 108

Scientific Notation Cornel Notes Ex. 6800 Changing from Standard Notation to Scientific Notation

Scientific Notation Cornel Notes Ex. 6800 Changing from Standard Notation to Scientific Notation 6800 1. Move decimal to get a number between 1 & 10 and count places moved. 3 2 1

Scientific Notation Cornel Notes Ex. 6800 Changing from Standard Notation to Scientific Notation 6800 1. Move decimal to get a number between 1 & 10 and count places moved. 3 2 1 68 x 103 2. Answer is a number between 1 & 10 times the power of ten ( places moved).

Ex. 6800 Changing from Standard Notation to Scientific Notation 6800 1. Move decimal to get a single digit # and count places moved 3 2 1 68 x 103 2. Answer is a single digit number times the power of ten of places moved. If the decimal is moved left the power is positive. If the decimal is moved right the power is negative.

Try This Ex. 720,000 Changing from Standard Notation to Scientific Notation

Try This Ex. 720,000 Changing from Standard Notation to Scientific Notation 720000 1. Move decimal to get a single digit # and count places moved. 5 4 3 2 1

Try This Ex. 720,000 Changing from Standard Notation to Scientific Notation 720000 1. Move decimal to get a single digit # and count places moved. 5 4 3 2 1 72 x 105 2. Answer is a number between 1 & 10 times the power of ten (# of places moved.

Scientific Notation Cornel Notes Ex. 4.5 x 10-3 Changing from Scientific Notation to Standard Notation

00045 Ex. 4.5 x 10-3 (Right if Pos. Left if Neg.) 3 2 1 Changing from Scientific Notation to Standard Notation Ex. 4.5 x 10-3 00045 1. Move decimal the same number of places as the exponent of 10. (Right if Pos. Left if Neg.) 3 2 1

Try This Ex. 8.9 x 105 Changing from Scientific Notation to Standard Notation

890000 Try This Ex. 8.9 x 105 (Right if Pos. Left if Neg.) 1 2 3 4 5 Changing from Scientific Notation to Standard Notation 890000 1. Move decimal the same number of places as the exponent of 10. (Right if Pos. Left if Neg.) 1 2 3 4 5

Addition and subtraction Scientific Notation 2.0 x 102 + 3.0 x 103 1. Make exponents of 10 the same 2. Add 0.2 + 3 and keep the 103 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x 107 - 6.3 x 105 2.0 x 107 -.063 x 107 = 2.0-.063 x 107 = 1.937 x 107 1. Make exponents of 10 the same 2. Subtract 2.0 - .063 and keep the 107 intact

Scientific Notation Makes These Numbers Easy 9.54x107 miles 1.86x107 miles per second