The Wonderful World of Metrics!

way of measuring things. The practice is the same, but different 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” foundation. Those units are…..  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

units. But how is that possible… 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) 1 kilometer = 1000 meters  HECTO (h) 1 Hectoliter = 100 liters  DECA (da) 1 Decagram = 10 grams  Remember Meters, Liters, Grams, and Seconds are the base units. They will be in every measurement.

r way to Pioneering the Prefixes base root word remember all this?  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 easier way remember all this? r way to

Can you Think of your own? 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 unit move the decimal to the left.  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.

K h da b d c m 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.

K h da b d c m 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.

K h da b d c m 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  Accuracy  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

Unit 1A.1 Assessment number 1 will cover all of the information on slides 2-13.

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 in an object. volume.  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

Wood Water Iron What is Density? If you take the same volume of different substances, then they will weigh different amounts. Wood Water Iron 1 1 1 0.50 g 1.00 g 8.00 g Q) Which of these is most dense? Why? cm3 cm3 cm3 IRON! It has the most mass for that volume.

of 1 g/cm3 Density for different things… own density. Substance Density (g/cm3)  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 Hydrogen 0.00009 Helium 0.000178 Air (atmospheric air) 0.001293 Carbon Monoxide 0.00125 Carbon Dioxide 0.001977 Gasoline 0.70 Ice 0.922 Water (@ 20deg C) 0.998 Water (@ 4deg C) 1.000 Milk 1.03 Magnesium 1.07 Water in the Dead Sea 1.24 (31.5% salt in the water) Aluminum 2.7 Iron 7.8 Lead 11.3 Mercury 13.6 Gold 19.3 (This is the only density you need to memorize!) Lead 21.4

Density for different things… Substance Density  Objects with different densities interact in a very predictable way  The more dense object will sink, the less dense will rise to the top… 3 (g/cm ) Hydrogen 0.00009 Helium 0.000178 Air (atmospheric air) 0.001293 Carbon Monoxide 0.00125 Carbon Dioxide 0.001977 Gasoline 0.70 Ice 0.922 Water (@ 20deg C) 0.998 Water (@ 4deg C) 1.000 Milk 1.03 Magnesium 1.07 Water in the Dead Sea 1.24 (31.5% salt in the water) Aluminum 2.7 Iron 7.8 Lead 11.3 Mercury 13.6 Gold 19.3 Lead 21.4

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

Find the mass of the object 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

space, calculate the 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:

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 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 Unknown: Density (g/cm3) Volume = 7 cm3 Formula: D = M / V Solution: D = 35g / 7cm3 D = 5g/cm3 To find density: . If the mass of an

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) 2.25 g/cm3 2) 22.5 g/cm3 3) 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 33 mL lecturePLUS Timberlake

Unit 1A.2 Assessment number 2 will cover all of the information on slides 15-31.

The Nature of Science (How Scientists Think)

Why Science? natural world we live in.  The goal of science is to understand the natural world we live in.

Why Hypothesize? explain what they think will happen in a certain  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.

questions meaningful. based on that question  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 fertilizer on plants. independent variable the  The factor you change on purpose  Example: The size of fertilizer on plants.  There can only be ONE independent variable the engine. The amount of  DEPENDENT VARIABLE  The result of what you changed  Example: The speed of the car. the plants. Growth rate of

Within the Experiment to make the comparison “fair”  CONSTANTS  Factors (variables) you try to keep the same 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. to

Within the Experiment group receives no treatment.  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.

 Take outliers into account. 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 think is happening. observe NOT what you senses  Your DATA is evidence  Evidence is what you think is happening.  Evidence can be:  Measured  Observed using one’s senses observe NOT what you  But you have to be observant!

Data measured and described with numbers. rate, speed, length, height,  QUANTITATIVE DATA  Results that can be with numbers.  Example: growth mass, volume  QUALITATIVE DATA measured and described rate, speed, length, height,  Results that are described our five senses.  Example: color, texture, in words. Results of “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 accepted, it will CONTINUE to be tested  Once a scientific idea becomes widely accepted, it will CONTINUE to be tested experimented on.  Every time an experiment is run, new information is learned and

Unit 1A.3 Assessment number 3 will cover all of the information on slides 33-52.

Scientific Notation

The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. 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.

For example: 4.5 x 103 The coefficient is _________. 4.5 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.

Rules to Remember! If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. positive left

Rules to Remember! If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. negative right

A number will have an exponent of zero if: ….the number is equal to or greater than 1, but less than 10.

1. Move the decimal to the right of the first non-zero number. 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 ANSWERS PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2 Put these numbers in scientific notation. PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2 1.2 x 101 9.87 x 10-1 5.96 x 102 7.0 x 10-7 1.0 x 106 1.26 x 10-3 9.88 x 1011 8 x 100 ANSWERS .00012 1000 0.01 12 .987 596 .000 000 7 1,000,000 .001257 987,653,000,000 8

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMS ANSWERS 4.9 X 102 3.75 X 10-2 5.95 X 10-4 9.46 X 103 3.87 X 101 7.10 X 100 8.2 X 10-5 490 .0375 .000595 9460 38.7 7.10 .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.

Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) 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

Sample Problem: Divide (6.4 x 106) by (1.7 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

Unit 1A.4 Assessment number 4 will cover all of the information on slides 54-67.

Unit 1A There will be a Unit Assessment covering all information in this PowerPoint.