LESSON 1 PHYSICAL QUANTITIES AND MEASUREMENT.pptx

Measurement

1. Physical Quantities and Measurements W eek 1 Lesson 1

2. L earning Outcomes The students will solve multi-concept, rich-content problems involving measurement using experimental and theoretical approaches. INTENDED LEARNING OUTCOMES MOST ESSENTIAL LEARNING COMPETENCY Solve measurement problems involving conversion of units, expression of measurements in scientific notation Differentiate accuracy from precision Differentiate random errors from systematic errors Estimate errors from multiple measurements of a physical quantity using variance

3. Table of Contents Accuracy and Precision Percent of Uncertainty Measurement Physical Quantity Base Quantity Derived Quantity Conversion of Units Significant Figures Scientific Notations Uncertainty Types of Uncertainty Estimating Uncertainties using Variance 1 3 4 2

4. KAHOOT! This can be the part of the presentation where you can introduce yourself, write your email…

5. Measurement 01

6. Measurement A process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The process of associating numbers with physical quantities and phenomena. It is fundamental to the sciences; to engineering, construction, and other technical fields; and to almost all everyday activities.

7. Physical Quantity Is a quantity that can be measured. It consists of a numerical magnitude and a unit. 25 m MAGNITUDE UNIT It can be classified as Base Quantity and Derived Quantity

8. Base Quantity Is a quantity that cannot be expressed in terms of other physical quantities. In order to work with a consistent and coherent measurement system, Système International d’Unitès or SI Units is used.

9. Derived Quantity Are quantities obtained from a combination of various base quantities and their units are determined from the relation between the base quantities and derived quantities.

10. Derived Quantity Are quantities obtained from a combination of various base quantities and their units are determined from the relation between the base quantities and derived quantities. Density  

11. Prefixes Are terms added before the units to indicate smaller or larger values. This is to avoid writing too many zeroes that may give rise to human error.

12. Conversion of Units 02

13. Conversion of Units If the physical quantity is not in the SI unit, it can be converted to SI unit using conversion factor .

14. Conversion of Units For Example, How many minutes are there in 3 hours? 3 hrs   180 mins CONVERSION FACTOR GIVEN UNIT CONVERTED UNIT

15. Scientific Notation Is a technique used to represent very small or large numbers with a numerical representation in the form of: N x 10 n Coefficient whose value is between 1-9 only Power of 10

16. Scientific Notation For Example How to express the following in the correct scientific notation? 123456 m 0.00123456 g Steps: Determine if the value is more or less than 1. If less than 1, its exponent is negative. If it's more than 1, the exponent is positive. If it is positive, move the decimal point to the LEFT to until the coefficient becomes 1-9 in value. If it is negative, move the decimal point to the RIGHT. Count the number of places you move the decimal point. This number is the exponent. 123456 m = 1.23456 x 10 5 m 0.00123456 g = 1.23456 x 10 -3 g

17. Scientific Notation For Example How to express the following scientific notation into numbers? 6.987 x 10 3 kg 9.2938 x 10 -5 m/s 2 Steps: If the exponent is positive, move the decimal to the RIGHT by the number of the exponent. If the exponent is negative, move to the LEFT by the number of exponent. 6.987 X 10 3 kg = 6987 kg 9.2938 x 10 -5 m/s 2 = 0.000092938 m/s 2

18. Operations on Scientific Notation Addition and Subtraction Step 1: Rewrite the numbers so that they all have the same power of ten by moving the decimal place of coefficient with the smaller exponent. Step 2: Add or subtract the numbers. Copy the power of ten. Step 3: Rewrite the sentence in a scientific notation. Example: 5.3×10 6 +11.2×10 7 Multiplication and Division Step 1: Multiply or Divide the coefficient Step 2: For multiplication, add the exponents. For division, subtract the exponent. Step 3: Rewrite the sentence in a scientific notation. Example:  

19. Significant Figures Is a method of reporting measured data or values to present more accurate data.

20. Accuracy and Precision 03

21. Accuracy and Precision Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other.

22. Uncertainties 04

23. Uncertainty These are measurements of physical quantities that tends to have mistakes or errors from its true value due to various factors. This can be caused by Systematic Errors or Random Errors Systematic Error Random Error Are due to the measuring device being biased in some way so that it reads consistently high or low. It can be Instrumental, personal and external errors Are due to the experimental or inherent difficulty in taking accurate measurements

24. How Number of Uncertainties be reported? 220 5 cm   Value of the quantity Number of uncertainty Unit This means, 220 cm + 5 = 225 cm 220 cm – 5 = 215 cm Range of true value

25. How to get Percent of Uncertainty? 220 5 cm   Solution, x 100 = 2.27%   Written as, 220 cm 2.27%  

26. Sample Problem The correct value of the measurement is between 200ml and 230ml. Find the percent uncertainty of the measurement and write the value correctly. Step 1 Determine the correct value and the number of uncertainty = 215 ml   215ml – 200ml = 15 230ml – 215ml = 15 Step 2 Calculate the Percent Uncertainty x 100 = 6.98%   Step 3 Write the correct value of the measurement 215 ml 6.98%  

27. Estimating Uncertainties of Multiple Measurement using Variance Step 1 Take the MEAN of the values Mean = = = 12.34   Step 2 Take the deviations of the values from the mean Measurements (cm) 12.30 12.35 12.31 12.34 12.36 12.38 12.33 12.35 Measurements (x-mean) Deviation (d) 12.30-12.34 -0.04 12.35-12.34 +0.01 12.31-12.34 -0.03 12.34-12.34 0.00 12.36-12.34 +0.02 12.38-12.34 +0.04 12.33-12.34 -0.01 12.35-12.34 +0.01

28. Estimating Uncertainties using Variance Step 3 Get the Average Deviation ( a.d. ) a.d. = = = 0.02   Step 4 Take the Average Deviations of the Mean (A.D.) Measurements (x-mean) Deviation (d) 12.30-12.34 -0.04 12.35-12.34 +0.01 12.31-12.34 -0.03 12.34-12.34 0.00 12.36-12.34 +0.02 12.38-12.34 +0.04 12.33-12.34 -0.01 12.35-12.34 +0.01 ∑x = 98.72 ∑𝑑 = 0.16 Note: Summation of the deviation without the regard of the sign. A.D. = = = 0.01 cm   Step 5 Write the Numerical value of the Uncertainty 12.34 0.01 cm   12.34 Mean (True Value) A.D. (Uncertainty) 0.01

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