Do NOW Please complete your Do NOW located in your packet I will collect it at the end of class in at end of class. Please work silently and independently

Scientific Notation

Objective SWBAT correctly convert from standard numbers into scientific notation, and back.

What is Scientific Notation? Scientific Notation is used to express very large and very small numbers more easily. It is a way of writing a number with “Powers of Ten” If number is greater than 1 : the Power of Ten is POSITIVE. If number is smaller than 1: the Power of Ten is NEGATIVE.

SN in Practice: Hope Diamond Made of the element Carbon Weight: 45 carats Weight: 9000 mg = 9 g Mass of one Carbon atom: 2X g 4.6X10 23 atoms LOTS OF ZEROS! TOO MUCH TO WRITE. $200–$250 million

RULES 1.23 x 10 4 NUMBER : Decimal always after first digit EXPONENT: Positive for big numbers, Negative for fractions! BASE: Always 10!

Conversion: #’s Greater than 1 Greater Than 1 1.Write a decimal after the first digit on the left 2.Count how many numbers are still after decimal and stop at original decimal point 3.Write the coefficient * 10 POSITIVE exp Example Hillary Clinton makes: Standard Notation: $186, per year Step 1: Step 2: Count 5 numbers to decimal Step 3: coefficient is 5 Answer: 1.86 x 10 5

Conversion: #’s Less than 1 Less than 1 1.Look where the decimal already is 2.Move the decimal to the right of the first non-zero digit 3.Count how many digits you moved 4.Write this as your base 10 NEGATIVE exp Example A germ is: centimeters long, convert to Sci Not. Step 1: 1.79 Step 2: moved 6 digits to the right Step 3: the exponent will be -6 (we moved to the right) Answer 1.79 x 10 -6

Guided Practice Chris Paul has 2,966 career assists. Write this in scientific notation Will Smith makes $35,000,000 per film. Write this in scientific notation.

Guided Practice LaDainian Tomlinson makes x 10 6 dollars/year. Write this in standard notation. 3,825,000 A human hair is 56 x meters thick. Write this in standard notation meters

Independent On your own, worksheet!

Adding and Subtracting in Scientific Notation

Adding and Subtracting… The important thing to remember about adding or subtracting is that the exponents must be the same! If the exponents are not the same then it is necessary to change one of the numbers so that both numbers have the same exponential value.

The general format for adding is as follows… (N x 10 x ) + (M x 10 x ) = (N + M) x 10 x The first step, if necessary, is to change one of the numbers so that both numbers have the same exponential value. Secondly, add the N and M numbers together and express as an answer. The final step is to multiply the result by the 10 x. (It may be necessary to put the resulting answer into proper scientific notation.) Adding and Subtracting…

Multiplying in Scientific Notation

Multiplying… The general format for multiplying is as follows… (N x 10 x )(M x 10 y ) = (N)(M) x 10 x+y First multiply the N and M numbers together and express an answer. Secondly multiply the exponential parts together by adding the exponents together. Finally multiply the two results for the final answer. (2.41 x 10 4 )(3.09 x 10 2 ) 2.41 x 3.09 = = 6 ***7.45 x 10 6***

Dividing in Scientific Notation

Dividing… The general format for dividing is as follows… (N x 10 x )/(M x 10 y ) = (N/M) x 10 x-y First divide the N number by the M number and express as an answer. Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number. Finally multiply the two results together to get the final answer. (4.89 x 10 7 )/(2.74 x 10 4 ) 4.89 / 2.74 = – 4 = 3 ***1.78 x 10 3***

Independent Practice On your own, worksheet!