Scientific Notation Helping us write really tiny or really big numbers

Carelessness when using numbers I have a million math problems to do I have a trillion things to get done tonight If you win 1 million dollars and you’re given the prize in 100 dollar bills, your stack of money is…. 4 inches high

However… If you win 1 trillion dollars and you’re given the prize in 100 dollar bills, your stack of money is…. 67 miles high

Rules to Scientific Notation Parts: 1. Coefficient (mantissa) – must be a number from 1 – Exponent – a power of x 10 6 Easier than writing 3,400,000

Numbers Greater Than Find the number by moving the decimal point that is between 1 – ,300,000  Write a positive exponent which is equal to the number of places you moved the decimal point to the left x 10 7

Numbers Less Than 1 1. Find the number by moving the decimal point that is between 1 –  Write a negative exponent which is equal to the number of places you moved the decimal point to the right x 10 -4

Math Operations & Sci. Notation For Multiplication: multiply coefficients add exponents (3.0 x 10 4 ) x (2.0 x 10 2 ) = 6.0 x x 2 = = 6

Math Operations & Sci. Notation For Division: divide coefficients subtract exponents (6.4 x 10 6) / (1.7 x 10 2 ) = 3.8 x / 1.7 = 3.86 – 2 = 4

Be Careful… Remember the rule about the coefficient! Ex. (4.0 x 10 3 ) x (3.0 x 10 4 ) = 12.0 x 10 7 WRONG!!! Answer = 1.2 x 10 8

Math Operations & Sci. Notation For Addition and Subtraction: must make the exponents the same Ex. 5.4 x x 10 4 = 0.54 x x x 10 4

Special Note Sometimes exponents are written differently. We are used to 3.4 x 10 5 However, you may see 3.4E5 It means the same thing (“E” represents the exponent and replaces x 10