Metric System

Scientific Process SkillsMeasurements

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 SystemProperty Name Symbol

Length Meter m

Volume(of a liquid)

Liter L

Force (weight)

Newton N

Mass Gram g

Temp *KelvinCelsius

KºC

How big are they?

King Henry

King = Kilo 1,000Henry = Hecto 100Died = Deka 10Unexpectedly = base unit 1 Drinking = Deci 1/10Chocolate = Centi 1/100Milk = 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. 

5.67 x 105 exponent

coefficient base

Scientific Notation

1. The coefficient must be greater than or equal to 1 and less than 10.

2. The base must be 10.

3. 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 5.676

The decimal will move 10 places to the left, making the exponent equal to 10.

Answer equals 5.676 x 1010

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 107 to standard notation.

  107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000

so,    6.03 x 107 = 6.03 x 10 000 000 = 60 300 000

OR

Since it is a positive 7, move the decimal 7 places to the right

Therefore, 6.03 x 107 = 60,300,000

Now we try a number that is very small

Change 0.000000902 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 103) x (4.54 x 106)

• (6.8 x 4.54) x (103 x 106)

• 30.872 x 109

• 3.0872 x 1010

Another Multiply

• (2.0 x 10-1) x (8.5 x 105)

• (2.0 x 8.5) x (10-1 x 105)

• 17 x 104

• 1.7 x 105

Example - Divide • Divide 3.5 x 108 by 6.6 x 104

• 3.5 x 108

6.6 x 104

• .530303 x 104

• 5.30303 x 103

Add

• (6.71 x 105) + (3.41 x 102)

• (6.71 x 105) + (.00341 x 105)

• 6.71341 x 105

Subtract

• (3.4067 x 105) – (6.7062 x 104)

• (3.4067 x 105) – (.67062 x 105)

• 2.7305 x 105