Helping us write really tiny or really big numbers 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 – 9.9 2. Exponent – a power of 10 3.4 x 106 Easier than writing 3,400,000

Numbers Greater Than 10 Find the number by moving the decimal point that is between 1 – 9.9 45,300,000  4.53 Write a positive exponent which is equal to the number of places you moved the decimal point to the left. 4.53 x 107

Numbers Less Than 1 Find the number by moving the decimal point that is between 1 – 9.9 0.000291  2.91 Write a negative exponent which is equal to the number of places you moved the decimal point to the right. 2.91 x 10-4

Math Operations & Sci. Notation For Multiplication: multiply coefficients add exponents (3.0 x 104) x (2.0 x 102) = 6.0 x 106 3 x 2 = 6 4 + 2 = 6

Math Operations & Sci. Notation For Division: divide coefficients subtract exponents (6.4 x 106) / (1.7 x 102) = 3.8 x 104 6.4 / 1.7 = 3.8 6 – 2 = 4

Be Careful… Remember the rule about the coefficient! Ex. (4.0 x 103) x (3.0 x 104) = 12.0 x 107 WRONG!!! Answer = 1.2 x 108

Math Operations & Sci. Notation For Addition and Subtraction: must make the exponents the same Ex. 5.4 x 103 + 6.0 x 104 = 0.54 x 104 +6.0 x 104 6.5 x 104

Special Note Sometimes exponents are written differently. We are used to 3.4 x 105 However, you may see 3.4E5 It means the same thing (“E” represents the exponent and replaces x 10