Metric System Scientific Process Skills Measurements

The metric system The metric system is a system of measurement used world-wide that is based on values of 10. This is sometimes referred to as SI units.

Metric System PropertyNameSymbol LengthMeterm Volume (of a liquid) LiterL Force (weight) NewtonN MassGramg Temp*Kelvin Celsius K ºC

How big are they?

King Henry K ing = Kilo 1,000 H enry = Hecto 100 D ied = Deka 10 U nexpectedly = base unit 1 D rinking = Deci 1/10 C hocolate = Centi 1/100 M ilk = Milli 1/1000

Stair Method or move decimal point to the left or move decimal point to the right

Scientific Notation Scientific notation is simply a short hand method for expressing, and working with, very large or very small numbers. Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent x 10 5  exponent coefficient base

Scientific Notation 1.The coefficient must be greater than or equal to 1 and less than The base must be The exponent must show the number of decimal places that the decimal needs to be moved to become standard notation.

Changing numbers from standard notation to scientific notation. When changing from standard notation to scientific notation, moving the decimal to the right means a ‘negative’ exponent and moving the decimal to the left is means a ‘positive’ exponent. Change 56,760,000,000 to scientific notation The decimal is at the end of the final zero Move the decimal behind the five to ensure that the coefficient is less than 10, but greater than or equal to one. The coefficient will then read The decimal will move 10 places to the left, making the exponent equal to 10. Answer equals x 10 10

Changing numbers from scientific notation to standard notation. (When changing from scientific notation to standard notation, a positive exponent indicates moving the decimal to the ‘right’, a negative exponent indicates moving the decimal to the ‘left’ ) Change 6.03 x 10 7 to standard notation = 10 x 10 x 10 x 10 x 10 x 10 x 10 = so, 6.03 x 10 7 = 6.03 x = OR Since it is a positive 7, move the decimal 7 places to the right Therefore, 6.03 x 10 7 = 60,300,000

Now we try a number that is very small Change to scientific notation The decimal must be moved behind the 9 to ensure a proper coefficient. The coefficient will be 9.02 The decimal moves seven spaces to the right, making the exponent -7 Answer equals 9.02 x 10 -7

Calculating with Scientific Notation Rule for Multiplication - When you multiply numbers with scientific notation, multiply the coefficients together and add the exponents. The base will remain 10. Rule for Division - When you divide numbers with scientific notation, divide the coefficients and subtract the exponents. The base will remain 10. Rule for Addition and Subtraction – when adding or subtracting in scientific notation, you must first get the numbers to the same power of 10. This will often involve changing the decimal place of the coefficient. Then add or subtract the coefficients and leave the base and exponent the same.

Example - Multiply (6.8 x 10 3 ) x (4.54 x 10 6 ) (6.8 x 4.54) x (10 3 x 10 6 ) x x 10 10

Another Multiply (2.0 x ) x (8.5 x 10 5 ) (2.0 x 8.5) x (10 -1 x 10 5 ) 17 x x 10 5

Example - Divide Divide 3.5 x 10 8 by 6.6 x x x x x 10 3

Add (6.71 x 10 5 ) + (3.41 x 10 2 ) (6.71 x 10 5 ) + ( x 10 5 ) x 10 5

Subtract ( x 10 5 ) – ( x 10 4 ) ( x 10 5 ) – ( x 10 5 ) x 10 5