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Learn to convert standard numbers into scientific notation and back, with practical examples and rules for adding, subtracting, multiplying, and dividing. Practice independently to enhance your skills!
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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
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: 2X10-23 g • 4.6X1023 atoms • LOTS OF ZEROS! TOO MUCH TO WRITE. $200–$250 million
RULES 1.23 x 104 EXPONENT:Positive for big numbers, Negative for fractions! BASE:Always 10! NUMBER: Decimal always after first digit
Conversion: #’s Greater than 1 Greater Than 1 Example Hillary Clinton makes: Standard Notation: $186,600.00 per year Step 1: 1.86600.00 Step 2: Count 5 numbers to decimal Step 3: coefficient is 5 Answer: 1.86 x 10 5 • Write a decimal after the first digit on the left • Count how many numbers are still after decimal and stop at original decimal point • Write the coefficient * 10 POSITIVE exp
Conversion: #’s Less than 1 Less than 1 Example A germ is: .00000179 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 • Look where the decimal already is • Move the decimal to the rightof the first non-zero digit • Count how many digits you moved • Write this as your base 10 NEGATIVEexp
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 3.825 x 10 6 dollars/year. Write this in standard notation. 3,825,000 • A human hair is 56 x 10 -6 meters thick. Write this in standard notation. 0.0000056 meters
Independent • On your own, worksheet!
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.
Adding and Subtracting… • The general format for adding is as follows… (N x 10x) + (M x 10x) = (N + M) x 10x • 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 10x. • (It may be necessary to put the resulting answer into proper scientific notation.)
Multiplying… • The general format for multiplying is as follows… (N x 10x)(M x 10y) = (N)(M) x 10x+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 104)(3.09 x 102) 2.41 x 3.09 = 7.45 4 + 2 = 6 ***7.45 x 106***
Dividing… • The general format for dividing is as follows… • (N x 10x)/(M x 10y) = (N/M) x 10x-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 107)/(2.74 x 104) 4.89 / 2.74 = 1.78 7 – 4 = 3 ***1.78 x 103***
Independent Practice • On your own, worksheet!
