Topic: Scientific Notation Essential Question: What is scientific notation and how is it used?

What is scientific notation? Definition: A number that is written as the product of a factor and a power of 10. The absolute value of the factor must be greater than or equal to 1 and less than 10. Example:

What is the purpose of scientific notation? It is often used to express very large or very small numbers. Example:

How is scientific notation converted to standard form? The exponent tells us how many spaces to move the decimal. A positive exponent implies a number greater than 1 in standard form. Example: 4.5 x 104 = 45,000 A negative exponent implies a number less than 1 in standard form. Example: 4.5 x 10-4 = 0.00045

How is addition/subtraction completed in scientific notation? Convert to standard notation, add/subtract, and convert back to scientific notation (if necessary). Example: (3 x 104) + (6 x 105) 30,000 + 600,000 630,000 = 6.3 x 105

How is multiplication completed in scientific notation? Use Associative Property to group the factors and powers of ten together. Multiply the factors normally. Use Product of Powers to simplify the powers of ten. Example: (3 x 108)(3 x 104) (3 x 3)(108 x 104) 9 x 108+4 9 x 1012

How is division completed in scientific notation? Use Associative Property to group the factors and powers of ten together. Divide the factors normally. Use Quotient of Powers to simplify the powers of ten. Example: 8.6 x 1012 = 8.6 x 1012 = 4.3 x 1012-4 2 x 104 2 104 = 4.3 x 108

Summary Scientific notation uses a factor and power of ten to express small & large #s. Scientific notation can be converted to standard form. Standard form is used to add/subtract. Associative Property & Exponent laws are used to multiply/divide in scientific notation.