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Understanding Mass vs. Weight: A Scientific Approach

Learn about matter, mass, and weight in this scientific guide. Explore the scientific method, steps, and significance of significant figures and scientific notation.

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Understanding Mass vs. Weight: A Scientific Approach

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  1. Scientific Method

  2. Mass vs. Weight • First we will define Matter… • Matter – anything that has mass & takes up space • Mass– measurement that tell how much matter you have (kg) • Weight – measurement of the amount of matter you have with the effect of gravity

  3. For Example… • Let’s say a guy weighs 150 pounds • This is about 54 kg in mass • What would his mass be on the moon if the moon’s gravity is about 1/6 that of the Earth?

  4. Hmmmm… • Would it be 1/6 of 150 pounds? • Would it be 1/6 of 54 kg? • Would it be 150 pounds • Or would it be 54 kg? The answer is … 54 kg

  5. Some of you are scratching your heads… • The reason is because gravity has NOTHING to do with mass – that’s only for weight • His mass did not change only his weight changed

  6. The Scientific Method • Scientific Method – a systematic approach used in scientific study • It is an organized approach for scientists to do research • Provides a method for scientists to verify their work and the work of others

  7. Steps for the Scientific Method Step # 1 – Observation • Observation – the act of gathering information (data) • Qualitative data – information with NO numbers • (hot, blue, rainy, cold) • Quantitative data – information with numbers • (98°F, 80% humidity, 0°C)

  8. Steps for the Scientific Method Step # 2 – Form a Hypothesis • Hypothesis – tentative explanation for what has been observed • There is no formal evidence at this point • It is just a gut feeling

  9. Steps for the Scientific Method Step # 3 – ExperimentationExperimentation – a set of controlled observations that test the hypothesis • Independent variable – the thing that you change in the experiment • Dependant variable – the thing that changes because you changes the independent variable • Constant – something that does not change during the experiment • Control – the standard for comparison

  10. For example… • Let’s say we are going to do an experiment testing what happens when you heat and cool a balloon… We will start with a balloon at room temperature

  11. Now we will change something… I will add heat to one balloon It will expand What will happen to the balloon’s size?

  12. Now let’s cool things down I will add cool down the balloon It will get smaller What will happen to the balloon’s size?

  13. So what is what? (Independent Variable) • What variable did YOU change? • Temperature • What variable changes BECAUSE you changed the temperature? • Size of the balloon • What is did not change in the experiment? • Amount of air in the balloon, what the balloon is made of… • What balloon did you use to compare the others to? • The room temperature balloon (Dependent Variable) (Constant) (Control)

  14. Steps for the Scientific Method Step # 4 – Conclusion • Conclusion – judgment based on the information obtained

  15. Introduction to Significant Figures& Scientific Notation

  16. Significant Figures • Scientist use significant figures to determine how precise a measurement is • Significant digits in a measurement include all of the known digits plus one estimated digit

  17. For example… • Look at the ruler below • Each line is 0.1cm • You can read that the arrow is on 13.3 cm • However, using significant figures, you must estimate the next digit • That would give you 13.30 cm

  18. Let’s try this one • Look at the ruler below • What can you read before you estimate? • 12.8 cm • Now estimate the next digit… • 12.85 cm

  19. The same rules apply with all instruments • The same rules apply • Read to the last digit that you know • Estimate the final digit

  20. Let’s try graduated cylinders • Look at the graduated cylinder below • What can you read with confidence? • 56 ml • Now estimate the last digit • 56.0 ml

  21. One more graduated cylinder • Look at the cylinder below… • What is the measurement? • 53.5 ml

  22. Rules for Significant figuresRule #1 • All non zero digits are ALWAYS significant • How many significant digits are in the following numbers? • 3 Significant Figures • 5 Significant Digits • 4 Significant Figures • 274 • 25.632 • 8.987

  23. Rule #2 • All zeros between significant digits are ALWAYS significant • How many significant digits are in the following numbers? 3 Significant Figures 5 Significant Digits 4 Significant Figures 504 60002 9.077

  24. Rule #3 • All FINAL zeros to the right of the decimal ARE significant • How many significant digits are in the following numbers? 3 Significant Figures 5 Significant Digits 7 Significant Figures 32.0 19.000 105.0020

  25. Rule #4 • All zeros that act as place holders are NOT significant • Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal

  26. 0.0002 6.02 x 1023 100.000 150000 800 1 Significant Digit 3 Significant Digits 6 Significant Digits 2 Significant Digits 1 Significant Digit For example How many significant digits are in the following numbers?

  27. Rule #5 • All counting numbers and constants have an infinite number of significant digits • For example: 1 hour = 60 minutes 12 inches = 1 foot 24 hours = 1 day

  28. 0.0073 100.020 2500 7.90 x 10-3 670.0 0.00001 18.84 2 Significant Digits 6 Significant Digits 2 Significant Digits 3 Significant Digits 4 Significant Digits 1 Significant Digit 4 Significant Digits How many significant digits are in the following numbers?

  29. Rules Rounding Significant DigitsRule #1 • If the digit to the immediate right of the last significant digit is less that 5, do not round up the last significant digit. • For example, let’s say you have the number 43.82 and you want 3 significant digits • The last number that you want is the 8 – 43.82 • The number to the right of the 8 is a 2 • Therefore, you would not round up & the number would be 43.8

  30. Rounding Rule #2 • If the digit to the immediate right of the last significant digit is greater that a 5, you round up the last significant figure • Let’s say you have the number 234.87 and you want 4 significant digits • 234.87 – The last number you want is the 8 and the number to the right is a 7 • Therefore, you would round up & get 234.9

  31. 200.99 (want 3 SF) 18.22 (want 2 SF) 135.50 (want 3 SF) 0.00299 (want 1 SF) 98.59 (want 2 SF) 201 18 136 0.003 99 Let’s try these examples…

  32. Significant Digits Calculations

  33. Significant Digits in Calculations • Now you know how to determine the number of significant digits in a number • How do you decide what to do when adding, subtracting, multiplying, or dividing?

  34. Rules for Addition and Subtraction • When you add or subtract measurements, your answer must have the same number of decimal places as the one with the fewest • For example: 20.4 + 1.322 + 83 = 104.722

  35. Addition & Subtraction Continued • Because you are adding, you need to look at the number of decimal places 20.4 + 1.322 + 83 = 104.722 (1) (3) (0) • Since you are adding, your answer must have the same number of decimal places as the one with the fewest • The fewest number of decimal places is 0 • Therefore, you answer must be rounded to have 0 decimal places • Your answer becomes • 105

  36. 1.23056 + 67.809 = 23.67 – 500 = 40.08 + 32.064 = 22.9898 + 35.453 = 95.00 – 75.00 = 69.03956  69.040 - 476.33  -476 72.1440  72.14 58.4428  58.443 20  20.00 Addition & Subtraction Problems

  37. Rules for Multiplication & Division • When you multiply and divide numbers you look at the TOTAL number of significant digits NOT just decimal places • For example: 67.50 x 2.54 = 171.45

  38. Multiplication & Division • Because you are multiplying, you need to look at the total number of significant digits not just decimal places 67.50 x 2.54 = 171.45 (4) (3) • Since you are multiplying, your answer must have the same number of significant digits as the one with the fewest • The fewest number of significant digits is 3 • Therefore, you answer must be rounded to have 3 significant digits • Your answer becomes • 171

  39. 890.15 x 12.3 = 88.132 / 22.500 = (48.12)(2.95) = 58.30 / 16.48 = 307.15 / 10.08 = 10948.845  1.09 x 104 3916.977  3917.0 141.954  142 3.5376  3.538 30.47123  30.47 Multiplication & Division Problems

  40. 18.36 g / 14.20 cm3 105.40 °C –23.20 °C 324.5 mi / 5.5 hr 21.8 °C + 204.2 °C 460 m / 5 sec = 1.293 g/cm3 = 82.20 °C = 59 mi / hr = 226.0 °C = 90 or 9 x 101 m/sec More Significant Digit Problems

  41. Scientific Notation • Scientific notation is used to express very large or very small numbers • I consists of a number between 1 & 10 followed by x 10 to an exponent • The exponent can be determined by the number of decimal places you have to move to get only 1 number in front of the decimal

  42. Large Numbers • If the number you start with is greater than 1, the exponent will be positive • Write the number 39923 in scientific notation • First move the decimal until 1 number is in front – 3.9923 • Now at x 10 – 3.9923 x 10 • Now count the number of decimal places that you moved (4) • Since the number you started with was greater than 1, the exponent will be positive • 3.9923 x 10 4

  43. Small Numbers • If the number you start with is less than 1, the exponent will be negative • Write the number 0.0052 in scientific notation • First move the decimal until 1 number is in front – 5.2 • Now at x 10 – 5.2 x 10 • Now count the number of decimal places that you moved (3) • Since the number you started with was less than 1, the exponent will be negative • 5.2 x 10 -3

  44. 99.343 4000.1 0.000375 0.0234 94577.1 9.9343 x 101 4.0001 x 103 3.75 x 10-4 2.34 x 10-2 9.45771 x 104 Scientific Notation Examples Place the following numbers in scientific notation:

  45. Going from Scientific Notation to Ordinary Notation • You start with the number and move the decimal the same number of spaces as the exponent. • If the exponent is positive, the number will be greater than 1 • If the exponent is negative, the number will be less than 1

  46. 3 x 106 6.26x 109 5 x 10-4 8.45 x 10-7 2.25 x 103 3000000 6260000000 0.0005 0.000000845 2250 Going to Ordinary Notation Examples Place the following numbers in ordinary notation:

  47. Conversions And Density Problems

  48. Accuracy vs. Precision • Accuracy – How close you are to the correct answer • Precision – How close your answers are together

  49. For Example… • Let’s say we had the following dart board Is the accuracy good or bad? Accuracy - GOOD Precision - GOOD Is the precision good or bad?

  50. Try this one • Let’s say we had the following dart board Is the accuracy good or bad? Accuracy - BAD Precision - GOOD Is the precision good or bad?

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