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# Measurement

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1. Measurement

2. Vocabulary Metric System Meniscus Mass Density Weight Volume Volume Displacement SI (International System of Units)

3. Measurement Systems • Measurement is fundamental to our society • Over 200 years ago, there were many different measurement systems • One of the first tools developed by humans was measurement 1

4. Measurement Systems “Weights and measures may be ranked among the necessaries of life to every individual of human society. They enter into the economical arrangements and daily concerns of every family. They are necessary to every occupation of human industry; to the distribution and security of every species of property; to every transaction of trade and commerce; to the labors of the husbandman; to the ingenuity of the artificer; to the studies of the philosopher; to the researches of the antiquarian; to the navigation of the mariner, and the marches of the soldier; to all the exchanges of peace, and all the operations of war. The knowledge of them, as in established use, is among the first elements of education, and is often learned by those who learn nothing else, not even to read and write.” JOHN QUINCY ADAMS - Report to the Congress, 1821 What if measurement tools and equipment did not exist?

5. Metric Units Kilo/ Hecto/ Deka/ (Base) Unit/ Deci/ Centi/ Milli King Henry Doesn't Usually Drink Chocolate Milk

6. Why is it important to have a standard system?

7. International System of Units (SI) • A version of the metric system used by scientists all over the world. • Systeme International d’Unites • Standard system of measurement that allows scientists to compare data and communicate with each other about their results. • Based on powers of 10 Powers of 10 video

8. SI Units Units: Length: Meter (m) Mass: Kilogram (kg) Time: Second (s) Temperature: Kelvin (K) Amount of Substance: Mole (mol) Electric Current: Ampere (A) Luminous Intensity: Candela (cd) Derived Units: Volume: cubic meter (m3) Density: grams per cubic centimeter (g/cm3) Others: Speed Force Pressure Energy

9. Common Measurement Tools Mass and Weight Volume Length

10. Length, Time and Temperature Length • SI unit = Meter (m) • Tools used to measure length: Meter stick, measuring tape, etc. Temperature • SI unit = Kelvin (k) • Tools used to measure temperature: thermometer. Time • SI unit = Second (s) • Tools used to measure time: stopwatch, clock, etc.

11. Temperature • A measure of the average energy of motion of the particles of a substance. • 3 scales used to measure temperature: Fahrenheit, Celsius, and Kelvin • On the Celsius scale, 0 = Freezing and 100 = Boiling • 0 Kelvin = Absolute Zero, the temperature at which no more heat can be removed- there is not a temperature that is colder. • Kelvin is the SI unit, and it is often used in science because it does not have negative numbers.

12. Temperature

13. What has more mass- a pound of feathers or a pound of rocks? Which is more dense?

14. Mass v. Weight Mass and Weight are not the same • Mass (the resistance to change in motion)-inertia • A measure of amount of matter an object contains. • Does not change when the object’s location is changed. • Measured using a triple-beam balance • SI unit is Kilogram (kg). • Weight (a force) • A measure of the force of gravity acting on an object. • Weight = mass x gravity • Weight does change depending on where an object is located. • SI unit is the Newton (N). Example: If you go to the moon with a rock with a mass of 200 grams (on Earth), it will still have a mass of 200 grams on the moon. However, the rock will feel lighter because the force of gravity is not as strong. It’s weight will be less.

15. Volume • Volume: is a measure of the amount of space an object occupies. • The SI unit for volume is the cubic meter (m3) Measuring Volume: use a graduated cylinder or a metric ruler • Liquids: Use a container with volume markings. Units are in Liters (l) or Milliliters (ml). • Solids: Volume= Length x Width x Height Volume = 5 cm x 6 cm x 10 cm = 300 cm3 • Irregular solids: Place the object in water and measure how much the water rises (displacement of water).

16. Density • Density: is a measure of how much mass is contained in a certain volume. • Density= mass/volume • It is a derived SI measurement from the measurements of mass and volume. • Density is a physical characteristic of a substance. • Example: If you have a small glass of water and compare the water’s density to that of a huge lake, you find that the density is the same. • The units of measurement are g/cm3

17. Math Skills Important for Science • Estimation • Accuracy and Precision • Significant Figures and Scientific Notation • Unit Conversion • Mean, Median, Mode, Range • Percent Error • Graphing and analyzing data

18. Estimation • An estimate is an approximation of a number based on reasonable assumptions. • It is not guessing. • It is based on known information. • Estimates are used by scientists when they cannot use exact numbers. • Examples: • Astronomers cannot measure the distance between the stars. They use indirect measurements and models • Park rangers cannot count all the trees in a forest. How could we estimate the number of students in the school if we did not know?

19. Accuracy and Precision • Accuracy: How close a measurement is to the true or accepted value. • Precision: How close a group of measurements are to each other. • Both accuracy and precision are important in measurements. • The more precise and accurate the measurements, the more reliable the data Why do measurements need to be precise and accurate?

20. Accuracy v. Precision http://www.batesville.k12.in.us/physics/apphynet/Measurement/Accuracy_Precision.html

21. Accuracy and Precision How to achieve accuracy and precision: • Use high quality measurement tools • Make measurements carefully • Repeat the measurement several times

22. Can numbers be exact? What about measurements-Why would there be uncertainty in our measurements?

23. Significant Figures • All the digits in a measurement that have been measured exactly, plus one digit whose value has been estimated are significant figures. • Values that are important in a measurement- they tell you how certain you are about a measurement. • The number of sig figs you write for a measurement tell you how precise your measurement is based on the equipment you are using. • The last digit tells others that you are not certain about that number-it is estimated.

24. Significant Figures • Measurements always have some level of uncertainty Measurements are uncertain due to: • Limitations in our measurement tools • Human error • Limitations in our ability to see and interpret measurements • Manufacturing process limitations • Every tool that you use will have a different number of significant figures because there is a different level of certainty

25. Measuring with Proper Sig Fig’s How would measurements using these two different graduated cylinders be different? 10 ml 10.0 ml

26. Measuring with Significant Figures • Measurements should only contain significant figures • Example: the measurement 5.36 cm has 3 significant figures; the 6 has been estimated. • In most cases zero’s are counted as significant figures. • Examples: • the measurement 10.5 g has ______________ significant figures. • The measurement 100,045.360 m has ____________ significant figures.

27. What would my data be reporting if I said my measurement was 10.453 g instead of 10.5g?

28. Why do we need to account for this uncertainty in measurements?

29. Scientific Notation -Helps reduce ambiguity in the significance of zeros in a measurement -Helps make it easier to work with really BIG or really small numbers http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html

30. Converting to Scientific Notation • Basic rule: The exponent in scientific notation is equal to the number of times you move the decimal to the left or right to produce a number between 1 and 10. • If you move it right – it is a negative exponent • EX. 0.06078 = 6.078 x 10-2 • If you move it left- it is a positive exponent • EX. 10,567 = 1.0567 x 104

31. Converting to Scientific Notation Write the following in scientific notation: • 0.32 • 345 • .00000045 • 32000000 • 32000000. • 5.31

32. Unit Conversion (Dimensional Analysis • To convert between units you must use a conversion factor. • The conversion factor is a fraction: • The numerator: the units that you want in your answer • The denominator: the units that you start with • Example 1: Convert 12 inches to centimeters. • Solution 1: 1 inch = 2.54 centimeters 12 in x 2.54 cm/1 in. = 30.48 cm

33. Unit Conversion cont. Example 2: Convert 25 kilograms to grams. Solution 2: 1 kg= 1,000 grams 25 kg x 1000 g/1 kg = ____________ g Example 3: Convert 485 centimeters to meters. Solution 3: ____________________________________________

34. Mean, Median, Mode Mean: the numerical average. It is calculated by adding up all the values in a set of data and dividing by the total number of values. Median: The middle number in a set of data. Mode: The number that appears most often in a list of numbers or data set.

35. Percent Error • Percent Error is a calculation used to determine how accurate or close to the true value an experimental value really is. Percent error = Difference between experimental value and true valuex 100% true value • The ideal percent error is very low, which indicates stronger accuracy.

36. Percent Error Example Sarah measured the length of the board to be 1.32 m. The board’s actual length is 1.25 m. What was the Sarah’s percent error? Answer: _____________________________________