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# Metric System Scientific Notation

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### Metric System Scientific Notation

1. 1. Metric System & Scientific Notation Chemistry August 20 th /21 st , 2009
2. 2. Metric System <ul><li>The metric system is based on a base unit that corresponds to a certain kind of measurement </li></ul><ul><ul><ul><li>Length = meter </li></ul></ul></ul><ul><ul><ul><li>Volume = liter </li></ul></ul></ul><ul><ul><ul><li>Weight (Mass) = gram </li></ul></ul></ul><ul><li>Prefixes plus base units make up the metric system </li></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>Centi + meter = Centimeter </li></ul></ul></ul><ul><ul><ul><li>Kilo + liter = Kiloliter </li></ul></ul></ul>
3. 3. Metric System <ul><li>The three prefixes that we will use the most are: </li></ul><ul><ul><li>Kilo= 1000 </li></ul></ul><ul><ul><li>centi = 1/100 (one hundredth) </li></ul></ul><ul><ul><li>milli= 1/1000 (one thousandth) </li></ul></ul><ul><li>How do you remember all of them? </li></ul><ul><li>Kissing Hairy Dark space dogs causes mono </li></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
4. 4. Metric System <ul><li>So if you needed to measure length you would choose meter as your base unit </li></ul><ul><ul><li>Length of a tree branch </li></ul></ul><ul><ul><ul><li>1.5 meters </li></ul></ul></ul><ul><ul><li>Length of a room </li></ul></ul><ul><ul><ul><li>5 meters </li></ul></ul></ul><ul><li>But what if you need to measure a longer distance, like from your house to school? </li></ul><ul><ul><li>Let’s say you live approximately 10 miles from school </li></ul></ul><ul><ul><ul><li>10 miles = 16093 meters </li></ul></ul></ul><ul><ul><li>16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: </li></ul></ul><ul><ul><ul><li>16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place) </li></ul></ul></ul>
5. 5. Typical Metric Units <ul><li>What metric unit would you use to measure the length of the room? </li></ul><ul><li>What metric unit would you use to measure the distance between the mall and school? </li></ul><ul><li>What metric unit would you use to measure your weight? </li></ul><ul><li>What metric unit would you use to measure the amount of liquid in a soda bottle? </li></ul><ul><li>What unit would you use to measure the amount of liquid in an eye dropper? </li></ul>
6. 6. Metric System <ul><li>These prefixes are based on powers of 10. What does this mean? </li></ul><ul><ul><li>From each prefix every “step” is either: </li></ul></ul><ul><ul><ul><li>10 times larger </li></ul></ul></ul><ul><ul><ul><ul><li>or </li></ul></ul></ul></ul><ul><ul><ul><li>10 times smaller </li></ul></ul></ul><ul><ul><li>For example </li></ul></ul><ul><ul><ul><li>Centimeters are 10 times larger than millimeters </li></ul></ul></ul><ul><ul><ul><li>1 centimeter = 10 millimeters </li></ul></ul></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
7. 7. Metric System <ul><ul><li>Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length </li></ul></ul><ul><ul><ul><li>1 centimeter = 10 millimeters </li></ul></ul></ul><ul><ul><ul><li>Example not to scale </li></ul></ul></ul>1 cm 40 41 41 40 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm
8. 8. Metric System <ul><li>For each “step” to right, you are multiplying by 10 </li></ul><ul><li>For example, let’s go from a base unit to centi </li></ul><ul><ul><li>1 liter = 10 deciliters = 100 centiliters </li></ul></ul><ul><ul><li>2 grams = 20 decigrams = 200 centigrams </li></ul></ul>( 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)
9. 9. Metric System <ul><li>An easy way to move within the metric system is by moving the decimal point one place for each “step” desired </li></ul><ul><ul><li>Example: change meters to centimeters </li></ul></ul><ul><ul><li>1 meter = 10 decimeters = 100 centimeters </li></ul></ul><ul><ul><li>or </li></ul></ul><ul><ul><li>1.00 meter = 10.0 decimeters = 100. centimeters </li></ul></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
10. 10. Metric System <ul><li>Now let’s try our previous example from meters to kilometers: </li></ul><ul><ul><li>16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers </li></ul></ul><ul><li>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) </li></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
11. 11. Metric System <ul><li>If you move to the left in the diagram, move the decimal to the left </li></ul><ul><li>If you move to the right in the diagram, move the decimal to the right </li></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
12. 12. Metric System <ul><li>Now let’s start from centimeters and convert to kilometers </li></ul><ul><ul><li>400000 centimeters = ? kilometers </li></ul></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
13. 13. Metric System <ul><li>Now let’s start from meters and convert to centimeters </li></ul><ul><ul><li>5 meters = ? centimeters </li></ul></ul><ul><li>Now let’s start from kilometers and convert to meters </li></ul><ul><ul><li>.3 kilometers = ? meters </li></ul></ul>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)
14. 14. Metric System <ul><li>Summary </li></ul><ul><ul><li>Base units in the metric system are meter, liter, gram </li></ul></ul><ul><ul><li>Metric system is based on powers of 10 </li></ul></ul><ul><ul><li>For conversions within the metric system, each “step” is 1 decimal place to the right or left </li></ul></ul><ul><ul><li>Using the diagram below, converting to the right, moves the decimal to the right and vice versa </li></ul></ul>Kilo (1000) Hecto (100) Deca (10) Base Units meter gram liter deci (1/10) centi (1/100) milli (1/1000)
15. 15. Scientific Notation <ul><li>Scientific notation is a way of expressing really big numbers or really small numbers. </li></ul><ul><li>For very large and very small numbers, scientific notation is more concise. </li></ul><ul><li>Scientific Notation always has two parts: </li></ul><ul><ul><li>A number between 1 and 9.9999… </li></ul></ul><ul><ul><li>A power of 10 </li></ul></ul><ul><li>N x 10 x </li></ul>
16. 16. Writing Scientific Notation <ul><li>Place the decimal point so that there is one non-zero digit to the left of the decimal point. </li></ul><ul><li>Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. </li></ul><ul><li>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. </li></ul><ul><li>Example: </li></ul><ul><ul><li>Given: 289,800,000 </li></ul></ul><ul><ul><li>Start with: 2.898 </li></ul></ul><ul><ul><li>Decimal needs to move 8 places to the right </li></ul></ul><ul><ul><li>Answer: 2.898 x 10 8 </li></ul></ul>