1.2 Measurements and Uncertainties

1. 1.2 Measurements and Uncertainties

2. 1.2.1 State the fundamental units in the SI system • In science, numbers aren’t just numbers. • They need a unit. We use standards for this unit. • A standard is: • a basis for comparison • a reference point against which other things can be evaluated • Ex. Meter, second, degree

3. 1.2.1 State the fundamental units in the SI system • The unit of a #, tells us what standard to use. • Two most common system: • English system • Metric system • The science world agreed to use the International System (SI) • Based upon the metric system.

4. 1.2.1 State the fundamental units in the SI system

5. Conversions in the SI are easy because everything is based on powers of 10 1.2.1 State the fundamental units in the SI system

6. Ex. Length. • Base unit is meter. Units and Standards

7. Common conversions • 2.54 cm = 1 in 4 qt = 1 gallon • 5280 ft = 1 mile 4 cups = 48 tsp • 2000 lb = 1 ton • 1 kg = 2.205 lb • 1 lb = 453.6 g • 1 lb = 16 oz • 1 L = 1.06 qt

8. Scientific Notation

9. 1.2.2 Distinguish between fundamental and derived units and give examples of derived units. • Some derived units don’t have any special names

10. 1.2.2 Distinguish between fundamental and derived units and give examples of derived units. • Others have special names

11. 1.2.2 Distinguish between fundamental and derived units and give examples of derived units. • A derived unit is a unit which can be defined in terms of two or more fundamental units. • For example speed(m/s) is a unit which has been derived from the fundamental units for distance(m) and time(s)

12. Scientific Notation • A short-hand way of writing large numbers without writing all of the zeros.

13. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

14. The Distance From the Sun to the Earth 149,000,000km

15. Step 1 • Move the decimal to the left • Leave only one number in front of decimal 93,000,000 = 9.3000000

16. Step 2 • Write the number without zeros 93,000,000 = 9.3

17. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

18. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

19. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

20. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

21. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

22. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

23. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

24. 6.27 x 106 9.01 x 104 6,270,000 90,100 Practice:Write in Standard Form Move the decimal to the right.

25. Accuracy, Precision and Significant Figures

26. Accuracy & Precision • Accuracy:      • How close a measurement is to the true value of the quantity that was measured. • Think: How close to the real value is it?

27. Accuracy & Precision • Precision:     • How closely two or more measurements of the same quantity agree with one another. • Think: Can the measurement be consistently reproduced?

28. Significant Figures • The numbers reported in a measurement are limited by the measuring tool  • Significant figures in a measurement include the known digits plus one estimated digit

29. Three Basic Rules • Non-zero digits are always significant. • 523.7 has ____ significant figures • Any zeros between two significant digits are significant. • 23.07 has ____ significant figures • A final zero or trailing zeros if it has a decimal, ONLY, are significant. • 3.200 has ____ significant figures • 200 has ____ significant figures

30. Practice • How many sig. fig’s do the following numbers have? • 38.15 cm _________ • 5.6 ft ____________ • 2001 min ________ • 50.8 mm _________ • 25,000 in ________ • 200. yr __________ • 0.008 mm ________ • 0.0156 oz ________

31. Exact Numbers • Can be thought of as having an infinite number of significant figures • An exact number won’t limit the math. • 1. 12 items in a dozen • 2. 12 inches in a foot • 3. 60 seconds in a minute

32. Adding and Subtracting  • The answer has the same number of decimal places as the measurement with the fewest decimal places.    25.2 one decimal place + 1.34 two decimal places 26.54  answer 26.5 one decimal place

33. Practice:Adding and Subtracting  • In each calculation, round the answer to the correct number of significant figures. • A. 235.05 + 19.6 + 2.1 =           1) 256.75  2) 256.8  3) 257     • B. 58.925 - 18.2 =           1) 40.725  2) 40.73  3) 40.7 
 

34. Multiplying and Dividing • Round to so that you have the same number of significant figures as the measurement with the fewest significant figures. 42 two sig figs x 10.8 three sig figs 453.6  answer 450 two sig figs

35. Practice:Multiplying and Dividing  • In each calculation, round the answer to the correct number of significant figures. • A. 2.19 X 4.2 = 1) 9    2) 9.2   3) 9.198  • B. 4.311 ÷ 0.07 =           1) 61.58    2) 62   3) 60

36. Practice work • How many sig figs are in each number listed? • A) 10.47020 D) 0.060 • B) 1.4030 E) 90210 • C) 1000 F) 0.03020 • Calculate, giving the answer with the correct number of sig figs. • 12.6 x 0.53 • (12.6 x 0.53) – 4.59 • (25.36 – 4.1) ÷ 2.317