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UNIT 3 MEASUREMENT

UNIT 3 MEASUREMENT. Scientific Notation. Scientific notation expresses numbers as a multiple of two factors: a number between 1 and10; and ten raised to a power, or exponent. 6.02 X 10 23. Scientific Notation.

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UNIT 3 MEASUREMENT

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  1. UNIT 3 MEASUREMENT

  2. Scientific Notation • Scientific notation expresses numbers as a multiple of two factors: a number between 1 and10; and ten raised to a power, or exponent. • 6.02 X 1023

  3. Scientific Notation • When numbers larger than 1 are expressed in scientific notation, the power of ten is positive. • 2500 = 2.5 X 103 • When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative. • .0025 = 2.5 X 10-3

  4. Convert Data into Scientific Notation • Change the following data into scientific notation. • The diameter of the Sun is 1 392 000 km. B. The density of the Sun’s lower atmosphere is 0.000 000 028 g/cm3.

  5. Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction. Convert Data into Scientific Notation

  6. Convert Data into Scientific Notation • Remove the extra zeros at the end or beginning of the factor. • Remember to add units to the answers.

  7. MEASUREMENT

  8. Measuring • The numbers are only half of a measurement. • It is 3 long. • 3 what. • Numbers without units are meaningless. • How many feet in a yard? • 3 ft • You always need a numerical and unitvalue!

  9. In 1795, French scientists adopted a system of standard units called the metric system. • In 1960, an international committee of scientists met to update the metric system. • The revised system is called the Système Internationale d’Unités, which is abbreviated SI.

  10. Units of Measurement • Throughout any natural science course we are going to deal with numbers. Numbers by themselves are meaningless. That is why need to have some sort of reference or standard to compare to. International System of Units or SI units, is based on the metric system.

  11. Prefixes of the SI Units • Since the SI Units are based upon the metric system, we use prefixes to change the quantity we are discussing about which use multiples of ten. • Some standard prefixes are: Examples: 1 megabyte = 1,000,000 bytes 1 microgram = 0.000001 grams

  12. The Metric System An easy way to measure

  13. The Metric System Decimal system Powers of 10 2 Parts : Prefix – how many multiples of 10 milli, centi, Mega, micro Base Unit - meter, liter, gram…… ex. Millimeter, centigram, kiloliter

  14. Base Units Length - meter ( m ) Mass - gram ( g ) Time - second ( s ) Temperature - Kelvin or ºCelsius (K or C ) Energy - Joules ( J ) Volume - Liter (L ) Amount of substance - mole ( mol )

  15. Prefixes

  16. Converting • how far you have to move on a chart, tells you how far, and which direction to move the decimal place. • You need the base unit : (meters, Liters,grams,) etc. • You need a chart! • You need a plan!

  17. Dr – uL Rule Down right upLeft 21.5 g = __________mg 21,500 345.6 m = ___________ km 0.3456

  18. k h D d c m Conversions • Change 5.6 m to millimeters • starts at the base unit and move three to the right. • move the decimal point three to the right 5 6 0 0

  19. k h D d c m Conversions • convert 25 mg to grams • convert 0.45 km to mm • convert 35 mL to liters • It works because the math works, we are dividing or multiplying by 10 the correct number of times

  20. Accuracy and Precision • When scientists make measurements, they evaluate both the accuracy and the precision of the measurements. • Accuracyrefers to how close a measured value is to an accepted value. • Precisionrefers to how close a series of measurements are to one another.

  21. Accuracy and Precision • Precision • A measurement of how well several determinations of the quantity agree. • Accuracy • The agreement of a measurement with the accepted value of the quantity.

  22. Accuracy and Precision • An archery target illustrates the difference between accuracy and precision.

  23. SIGNIFICANT FIGURES

  24. Significant Figures Let’s take a look at some instruments used to measure --Remember: the instrument limits how good your measurement is!!

  25. Uncertainty in Measurements Different measuring devices have different uses and different degrees of accuracy.

  26. 1 2 3 4 5 Significant figures (sig figs) • We can only MEASURE at the lines on the measuring instrument • We can (and do) always estimate between the smallest marks. in

  27. 1 2 3 4 5 4 inches 4.5 inches What was actually measured? What was estimated? 0.5 inches in

  28. 1 2 3 4 5 Significant figures (sig figs) • The better marks… the better we can measure. • Also, the closer we can estimate 1 2 3 4 5 in in

  29. 1 2 3 4 5 4.5 inches 4.55 inches What was actually measured? What was estimated? 0.05 inches in

  30. So what does this all mean to you? • Whenever you make a measurement, you should be doing three things…… • Check to see what the smallest lines (increments) on the instrument represent • Measure as much as you can (to the smallest increment allowed by the device) • Estimate one decimal place further than you measured

  31. Decimal Places Review 23456.789 ten thousands thousandths ones tens hundredths hundreds tenths thousands Your estimate MUST always be one (and only one) decimal place further to the right than your measurement

  32. Practice Your graduated cylinder can only accurately measure to tens of mL. To what decimal place should you estimate? A balance can accurately measure to hundredths of grams. What decimal place will your estimate be?

  33. Work Backwards Now Look at the following measurements and determine the smallest increment that the measuring instrument could accurately measure to. Keep in mind that the last significant figure is the estimate. 100.3 g 207 L 1500 cm 0.0004467 kg ones tens thousands One-hundred thousandths

  34. What is measured and what is estimated in the following measurements?(Remember, significant figures include measured & estimated digits ) 100.3 207 1500 0.0004467 4 Sig Figs ; Measured: 100. ; Estimated: 0.3 3 Sig Figs ; Measured: 2.0 X 102 ; Estimated: 7 2 Sig Figs ; Measured: 1000 ; Estimated: 500 4 Sig Figs ; Measured: 0.000446; Est: 0.0000007

  35. SIGNIFICANT FIGURES The RULES

  36. Significant Figures • The term significant figures refers to digits that were measured. • When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

  37. Significant Figures • All nonzero digits are significant. • Zeroes between two significant figures are themselves significant. • Zeroes at the beginning of a number are never significant. • Zeroes at the end of a number are significant if a decimal point is written in the number.

  38. Significant FiguresWhat about the Zeros??

  39. Significant Figures in Calculations • When addition or subtraction is performed, answers are rounded to theleast significant decimal place. • When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.

  40. Sig figs. • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

  41. Sig. Fig. Calculations Multiplication/Division • Rules: • The measurement w/ the smallest # of sig. figs determines the # of sig. figs in answer • Let’s Practice!!! • 6.221cm x 5.2cm = 32.3492 cm2 4 2 • How many sig figs in final answer??? • And the answer is…. 32 cm2

  42. 27.93 + 6.4 = 27.93 + 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place = 34.3

  43. Practice • 4.8 + 6.8765= • 520 + 94.98= • 0.0045 + 2.113= • 6.0 x 102 - 3.8 x 103 = • 5.4 - 3.28= • 6.7 - .542= • 500 -126= • 6.0 x 10-2 - 3.8 x 10-3=

  44. DIMENSIONAL ANALYSIS

  45. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  46. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  47. Dimensional Analysis • Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  48. qt mL  Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  49. lb cm3 Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

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