Measurement I Units of Measurement p 34 45

Measurement I. Units of Measurement (p. 34 -45) w Number vs. Quantity w SI Base Units & Prefixes w Derived Units w Density Calculations

Number vs. Quantity ö Quantity - number + unit UNITS MATTER!!

Measurement is central to Physics ö Metric system: the set of units used for scientific measurements. ö SI Units: there are seven base SI units and all other units are derived from these.

SI Units Quantity Base Unit Symbol meter m Mass kilogram kg Time second s Temp kelvin K ampere A Length Current

SI Units Prefix Symbol Factor megakilodecicentimillimicronanopico- M k d c m n p 106 103 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

How confident are we in our measurements? ö Are they ACCURATE? ö Are they PRECISE? ö How many of the numerals in the measurement are SIGNIFICANT DIGITS?

Accuracy Closeness of a single value to the true value Precision Closeness of a set of values to each other

Precision and Accuracy

Uncertainty in Measurement ö All scientific measures are subject to error. ö The number of digits reported reflect the accuracy of the measurement and the precision of the measuring device. ö Significant Figures (Sig Figs) are all the figures known with certainty plus one extra uncertain figure.

Uncertainty in Measurement Instrument error Human error meniscus

Measurement on Metric Ruler 93. 55 cm 97. 18 cm

Rules: Significant Figures (Sig Figs) ö All non-zero numbers are significant. w Ex) 3. 45 l (3 sig fig) ö Zeros between non-zero numbers are significant. w Ex) 4, 503 l (4 sig fig) ö Zeros to the left of the first non-zero digit are not significant. w Ex) 0. 0003 l (1 sig fig) ö Zeros to the right of a nonzero digit are significant IF the number contains a decimal point.

Significant Figures (Sig Figs) 1. 23 grams = 0. 000123 grams = 2. 0 grams = 0. 020 grams = 100. grams = 3 3 2 2 1 3

How many Significant Figures ö 0. 00821 ö 630 ö 5020 ö 9102 ö 7. 200 x 102

How many Significant Figures ö 0. 00821 ö 630 ö 5020 ö 9102 ö 7. 200 x 102 Three Two Three Four

How many Significant Figures 0. 09430 5760 5002 5200 1. 30 x 105

How many Significant Figures 0. 09430 5760 5002 5200 1. 30 x 105 Four Three Four Two Three

Rounding off If the first insignificant digit is > 5 round up = 5 round up < 5 round down

Round off to three significant digits 546847

Round off to three significant digits last significant 546847 first insignificant

Round off to three significant digits 547000 546847 546000 Round up or Round down

Round off to three significant digits 547000 546847 546000 Round up

Round off to three significant digits ö 6876 ö 6874 ö 544. 5 ö 321. 5

Round off to three significant digits ö 6876 ö 6880 ö 6874 ö 6870 ö 544. 5 ö 545 ö 321. 5 ö 322

Scientific Notation ö For extremely large or small numbers ö Powers of 10 Speed of light is 30, 000, 000 cm/s ØMove decimal to the left 10 spaces Ø 30, 000, 000 cm/s Ø 3 x 1010 cm/s Ex) Wavelength of yellow light is 0. 000059 cm ØMove decimal to the right 5 spaces Ø 0. 000059 cm Ø 5. 9 x 10 -5 cm ö Ex) ö

Scientific Notation ö Correct Scientific Notation: 5. 20 x 104 ö Incorrect Scientific Notation: 520 x 102 ö Practice: Write in Scientific Notation. Ø 6, 200, 000, 000 = 6. 2 x 1015 Ø 0. 000000074 = 7. 4 x 10 -8

Significant Figures in Calculations ö Multiplication & Division w Fewest significant digits w 5. 231 x 2. 7 = 14 ö Addition & Subtraction w Least precise w 658. 2 - 144 = 514

III. Unit Conversions SI Prefix Conversions w Dimensional Analysis

A. SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

A. SI Prefix Conversions 532 m NUMBER UNIT 0. 532 km = _______ = NUMBER UNIT

move right move left A. SI Prefix Conversions Prefix Symbol Factor megakilodecicentimillimicronanopico- M k d c m n p 106 103 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

A. SI Prefix Conversions 1) 20 cm = 0. 2 _______ m 32 2) 0. 032 A = _______ m. A 3) 45 m = 45, 000 _______ nm 0. 0805 4) 805 dm = _______ km

B. Dimensional Analysis ö The “Factor-Label” Method w Units, or “labels” are canceled, or “factored” out

B. Dimensional Analysis ö 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.

B. Dimensional Analysis ö Lining up conversion factors: 1 in = 2. 54 cm =1 2. 54 cm 1 in = 2. 54 cm 1= 1 in

B. Dimensional Analysis ö Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? cm 8 cm 1 in 2. 54 cm in = 3. 15 in

B. Dimensional Analysis ö How many milliliters are in 1 quart of milk? qt m. L 1 qt 1 L 1000 m. L 1. 057 qt 1 L = 946 m. L

B. Dimensional Analysis 5) Assume your mass is 55 kg. How many pounds do you weigh? kg lb 55 kg 2. 2 lb 1 kg = 121 lb

B. Dimensional Analysis 6) How many feet long is a 5 K (5 km) race? km 5 km ft 1 mi 5280 ft 1. 609 km 1 mi = 16, 408 ft

B. Dimensional Analysis 7) How many grams does a 10 -lb. bag of potatoes weigh? lb g 10 lb 1 kg 1000 g 2. 2. lb 1 kg = 4545 g

B. Dimensional Analysis 8) Taft football needs 550 cm for a 1 st down. How many yards is this? cm 550 cm yd 1 in 1 ft 1 yd 2. 54 cm 12 in 3 ft = 6. 01 yd