+ Metric System & Scientific Notation Chemistry August 20 th /21 st, 2009

+ Metric System The metric system is based on a base unit that corresponds to a certain kind of measurement Length = meter Volume = liter Weight (Mass) = gram Prefixes plus base units make up the metric system Example: Centi + meter = Centimeter Kilo + liter = Kiloliter

+ Metric System The three prefixes that we will use the most are: Kilo= 1000 centi = 1/100 (one hundredth) milli= 1/1000 (one thousandth) How do you remember all of them? Kissing Hairy Dark space dogs causes mono Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)

+ Metric System So if you needed to measure length you would choose meter as your base unit Length of a tree branch 1.5 meters Length of a room 5 meters But what if you need to measure a longer distance, like from your house to school? Let’s say you live approximately 10 miles from school 10 miles = meters is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: meters = kilometers (or 16.1 if rounded to 1 decimal place)

+ Typical Metric Units What metric unit would you use to measure the length of the room? What metric unit would you use to measure the distance between the mall and school? What metric unit would you use to measure your weight? What metric unit would you use to measure the amount of liquid in a soda bottle? What unit would you use to measure the amount of liquid in an eye dropper?

+ Metric System These prefixes are based on powers of 10. What does this mean? From each prefix every “step” is either: 10 times larger or 10 times smaller For example Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)

+ Metric System Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 1 mm 1 cm

+ Metric System For each “step” to right, you are multiplying by 10 For example, let’s go from a base unit to centi 1 liter = 10 deciliters = 100 centiliters 2 grams = 20 decigrams = 200 centigrams ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200) Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)

+ Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Metric System An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters

+ Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Metric System Now let’s try our previous example from meters to kilometers: meters = decameters = hectometers = kilometers So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)

+ Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Metric System If you move to the left in the diagram, move the decimal to the left If you move to the right in the diagram, move the decimal to the right

+ Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Metric System Now let’s start from centimeters and convert to kilometers centimeters = ? kilometers

+ Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000) Metric System Now let’s start from meters and convert to centimeters 5 meters = ? centimeters Now let’s start from kilometers and convert to meters.3 kilometers = ? meters

+ Metric System Summary Base units in the metric system are meter, liter, gram Metric system is based on powers of 10 For conversions within the metric system, each “step” is 1 decimal place to the right or left Using the diagram below, converting to the right, moves the decimal to the right and vice versa Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)

+ Scientific Notation Scientific notation is a way of expressing really big numbers or really small numbers. Scientific notation is a way of expressing really big numbers or really small numbers. For very large and very small numbers, scientific notation is more concise. For very large and very small numbers, scientific notation is more concise. Scientific Notation always has two parts: A number between 1 and … A number between 1 and … A power of 10 A power of 10 N x 10 x

+ Writing Scientific Notation Place the decimal point so that there is one non-zero digit to the left of the decimal point. Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. Example: Given: 289,800,000 Given: 289,800,000 Start with: Start with: Decimal needs to move 8 places to the left Decimal needs to move 8 places to the left Answer: x 10 8 Answer: x 10 8

+ Try this: Given: Given: Start with: Decimal needs to move: Answer:

+ Change Scientific Notation back to Standard Form Simply move the decimal point to the right for positive exponent 10. Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.) Example: Example: Given: x 10 6 Given: x 10 6 Move: 6 places to the right (positive) Move: 6 places to the right (positive) Answer: 5,093,000 Answer: 5,093,000

+ Try This: Given: x Given: x Move: Move: Answer: Answer: