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The Wonderful World of Metrics! Introduction The metric system is a different way of measuring things. The practice is the same, but different units are involved. Can you think of any metric measurements that you have seen or heard? The “Basics” The metric system uses SI base units as a foundation. Those units are….. Meter (m) – a measure of distance Liter (L) – a measure of volume Kilogram (kg) – a measure of mass (this is the only one that uses a prefix! More on that soon…) Second (s) – a measure of time Kelvin (K) – a measure of temperature Mole (mol) – a measure of an amount The “Basics” Every measurement will include one of the base words. The metric system uses Prefixes too. Every prefix is related to the base units. But how is that possible… Pioneering the Prefixes Lets start with the prefixes for large measurements…. KILO (k) HECTO (h) DECA (da) 1 kilometer = 1000 meters 1 Hectoliter = 100 liters 1 Decagram = 10 grams Remember Meters, Liters, Grams, and Seconds are the base units. They will be in every measurement. Pioneering the Prefixes How about the small measurements… DECI (d) – 1 decimeter = 1/10 meter CENTI (c) – 1 centiliter = 1/100 liter MILLI (m) – 1 milligram = 1/1000 gram Remember, these prefixes are always added to the base root word But that’s so confusing….isn’t there an easierr way to remember all this? Good ol’ King Henry King Henry Died by Drinking Chocolate Milk Kilo Hecto Deca Base Deci Centi Milli Can you Think of your own? Converting Skillz When you are converting from one unit to another unit First figure out what you are starting with Then where (which direction) you are going! If you move to the right (aka big to small) then you move the decimal to the right. If you move to the left (aka small to big) then you move the decimal to the left. Practice makes Perfect! Try this one. 1 meter = hectometer 1st- Figure out your starting point and where you are going! K h da b d c m 2nd – Find the Decimal and move it the same way and number you moved in step 1. Practice makes Perfect! And this one. 2.5 kilograms = grams 1st- Figure out your starting point and where you are going! K h da b d c m 2nd – Find the Decimal and move it the same way and number you moved in step 1. Practice makes Perfect! Last one! 17.504 deciliters = decaliters 1st- Figure out your starting point and where you are going! K h da b d c m 2nd – Find the Decimal and move it the same way and number you moved in step 1. Precision vs Accuracy Precision A measure of the degree to which the measurements made (and made in the same way) agree with each other Accuracy Degree to which the experimental value agrees with the true or accepted value So, can measurements be precise without being accurate? Precision vs Accuracy Density Comparing Feathers and Rocks Which do you think would have the greater mass? Which do you think would have the greater volume? 1 kg of feathers 1 kg of rock Density Density is defined as mass per unit volume. Density is a measure of how tightly packed molecules are in an object. Basically, it is the amount of matter within a certain volume. The Math… The Units: Mass = Grams (g) Volume (2 ways) Ruler = cm3 Displacement = ml Density (2 ways) Ruler = g/cm3 Displacement = g/ml What is Density? If you take the same volume of different substances, then they will weigh different amounts. Water Iron 1 cm3 1 cm3 1 cm3 0.50 g 1.00 g 8.00 g Wood Q) Which of these is most dense? Why? IRON! It has the most mass for that volume. Density for different things… Substance Each substance has it’s own density. It does not matter how much of a substance you have, it will have the same density. 1 gram of water will have the same density as 100 grams of water Distilled Water has a density of 1 g/cm3 (This is the only density you need to memorize!) Hydrogen Helium Air (atmospheric air) Carbon Monoxide Carbon Dioxide Gasoline Ice Water (@ 20deg C) Water (@ 4deg C) Milk Magnesium Water in the Dead Sea (31.5% salt in the water) Aluminum Iron Lead Mercury Gold Lead Density (g/cm3) 0.00009 0.000178 0.001293 0.00125 0.001977 0.70 0.922 0.998 1.000 1.03 1.07 1.24 2.7 7.8 11.3 13.6 19.3 21.4 Density for different things… Substance Objects with different densities interact in a very predictable way The more dense object will sink, the less dense will rise to the top… Density (g/cm3) Hydrogen Helium Air (atmospheric air) Carbon Monoxide Carbon Dioxide Gasoline Ice Water (@ 20deg C) Water (@ 4deg C) Milk Magnesium Water in the Dead Sea (31.5% salt in the water) Aluminum Iron Lead Mercury 0.00009 0.000178 0.001293 0.00125 0.001977 0.70 0.922 0.998 1.000 1.03 1.07 1.24 Gold Lead 19.3 21.4 2.7 7.8 11.3 13.6 Different objects have different densities Is the ice or the water more dense? The water is more dense than the ice because the ice floats! Objects with more than 1 g/cm3 density will sink in tap water (ex: gold at 19.3) Objects with less than 1 g/cm3 density will float in tap water (ex: ice at 0.93) Sidenote… Sulfur hexaflouride. Density? Explain this. The Math… The Units: Mass = Grams (g) Volume (2 ways) Ruler = cm3 Displacement = ml Density (2 ways) Ruler = g/cm3 Displacement = g/ml Determining Density Step 1: Find the mass of the object Determining Density STEP 2: Determine Volume We have 2 ways to determine VOLUME. Measure Cube = L * W * H Cylinder = Πr2H Sphere = (4Πr3)/3 Calculate Displacement Displacement is how much liquid is moved out of the way to make room for the object placed in water Determining Density Step 3: Calculate Density = Mass Volume Units: For ruler: g/cm3 For displacement: g/ml To find density: 1) Find the mass of the object 2) Find the volume of the object 3) Divide : Density = Mass / Volume Ex. If the mass of an object is 35 grams and it takes up 7 cm3 of space, calculate the density. To find density: 1) Find the mass of the object 2) Find the volume of the object 3) Divide : Density = Mass / Volume Ex. If the mass of an object is 35 grams and it takes up 7 cm3 of space, calculate the density. Set up your density problems like this: Known: Mass = 35 grams Volume = 7 cm3 Unknown: Density (g/cm3) Formula: D = M / V Solution: D = 35g / 7cm3 D = 5g/cm3 Practice Problem 1 Osmium is a very dense metal. What is its density in g/cm3 if 50.00 g of the metal occupies a volume of 2.22cm3? 1) 2) 3) 2.25 g/cm3 22.5 g/cm3 111 g/cm3 Practice Problem #3 17 What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? A) 0.2 g/ cm3 B) 6 g/cm3 C) 252 g/cm3 25 ml lecturePLUS Timberlake 33 mL The Nature of Science (How Scientists Think) Why Science? The goal of science is to understand the natural world we live in. Why Hypothesize? Scientist hypothesize in order to try to explain what they think will happen in a certain situation Long-held assumptions should be questioned! How do you achieve Scientific success? Be creative: think outside the box! Those “Creative” experiments end up being the best ones. Persevere: If at first you don’t succeed, try, try, try again! If you did succeed, do it again to make sure it was correct in the first place. Question everything, but make your questions meaningful. You must be able to create an EXPERIMENT based on that question Scientific Inquiry 1. Observing / Come up with a question 2. Asking questions / doing research 3. Forming a hypothesis Hypothesis = educated guess BASED ON RESEARCH 4. Testing the hypothesis (Performing the experiment) Within the Experiment INDEPENDENT VARIABLE The factor you change on purpose Example: The size of the engine. The amount of fertilizer on plants. There can only be ONE independent variable DEPENDENT VARIABLE The result of what you changed Example: The speed of the car. Growth rate of the plants. Within the Experiment CONSTANTS Factors (variables) you try to keep the same to make the comparison “fair” Example: Test the speed of the car on the same track with the same car. Same amount of water & light for the plants. Within the Experiment CONTROL GROUP An experiment where one group receives no treatment. This group is used for comparison. Example: Speed of a car that did not get a larger engine. Growth rate of a plant that did not get any fertilizer. EXPERIMENTAL GROUP The group that has had the independent variable added to it. Example: The car with the bigger engine. Growth rate of a plant that did receive fertilizer. Within the Experiment Scientists ALWAYS confirm results REPEATED TRIALS Repeat the experiment to increase confidence in your results. Average the results to reduce random error. Take outliers into account. More Data = Better Results! 5. Gathering data More Data = Better Results! Evidence / Data Your DATA is evidence Evidence is what you observe NOT what you think is happening. Evidence can be: Measured Observed using one’s senses But you have to be observant! Data QUANTITATIVE DATA Results that can be measured and described with numbers. Example: growth rate, speed, length, height, mass, volume QUALITATIVE DATA Results that are described in words. Results of our five senses. Example: color, texture, “looks healthier”, “feels softer”, “smells burnt” 6. Conclusion Restate your hypothesis, and state whether your data supported or rejected the hypothesis 7. Sharing what has been learned Communicate your data with colleagues Publishing in journals Science is always tested Once a scientific idea becomes widely accepted, it will CONTINUE to be tested and experimented on. Every time an experiment is run, new information is learned Scientific Notation Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms. Scientists can work with very large and very small numbers more easily if the numbers are written in scientific notation. How to Use Scientific Notation • In scientific notation, a number is written as the product of two numbers….. …..a coefficient and 10 raised to a power. 4.5 x 103 The number 4,500 is written in scientific notation as ________________. The coefficient is _________. 4.5 The coefficient must be a number greater than or equal to 1 and smaller than 10. The power of 10 or exponent in this example is ______. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500. If a number is greater than 10, the exponent will be positive _____________ and is equal to the number of places the decimal must be moved to left the ________ to write the number in scientific notation. If a number is less than 10, the exponent will be negative _____________ and is equal to the number of places the decimal must be moved to right the ________ to write the number in scientific notation. A number will have an exponent of zero if: ….the number is equal to or greater than 1, but less than 10. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive. Practice Problems Put these numbers in scientific notation. PROBLEMS 1) .00012 2) 1000 3) 0.01 4) 12 5) .987 6) 596 7) .000 000 7 8) 1,000,000 9) .001257 10) 987,653,000,000 11) 8 ANSWERS 1) 1.2 x 10-4 2) 1 x 103 3) 1 x 10-2 4) 1.2 x 101 5) 9.87 x 10-1 6) 5.96 x 102 7) 7.0 x 10-7 8) 1.0 x 106 9) 1.26 x 10-3 10) 9.88 x 1011 11) 8 x 100 EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMS ANSWERS 1) 4.9 X 102 1) 490 2) 3.75 X 10-2 2) .0375 3) 5.95 X 10-4 3) .000595 4) 9.46 X 103 4) 9460 5) 3.87 X 101 5) 38.7 6) 7.10 X 100 6) 7.10 7) 8.2 X 10-5 7) .000082 Using Scientific Notation in Multiplication, Division, Addition and Subtraction Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules. Multiplication When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5 Answer: 6.7 x 102 Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2 Answer: 3.8 x 104 Addition and Subtraction To add or subtract numbers written in scientific notation, you must….express them with the same power of ten. Sample Problem: Add (5.8 x 103) and (2.16 x 104) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 103 = .58 x 104 so .58 x 104 + 2.16 x 104 =? Answer: 2.74 x 104