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

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

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

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

SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12

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

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

Precision and Accuracy

Uncertainty in Measurement All scientific measures are subject to error. The number of digits reported reflect the accuracy of the measurement and the precision of the measuring device. 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) All non-zero numbers are significant. Ex) 3.45 (3 sig fig) Zeros between non-zero numbers are significant. Ex) 4,503 (4 sig fig) Zeros to the left of the first non-zero digit are not significant. Ex) 0.0003 (1 sig fig) Zeros to the right of a nonzero digit are significant IF the number contains a decimal point. Ex) 1.90 Ex) 10,300

Significant Figures (Sig Figs) 1.23 grams = 3 0.000123 grams = 3 2.0 grams = 2 0.020 grams = 2 100 grams = 1 100. grams = 3

How many Significant Figures 0.00821 630 5020 9102 7.200 x 102

How many Significant Figures 0.00821 630 5020 9102 7.200 x 102 Three Two 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 Two

> 5 round up = 5 round up < 5 round down 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 Round up 546847 or 546000 Round down

Round off to three significant digits 547000 Round up 546847 546000

Round off to three significant digits 6876 6874 544.5 321.5

Round off to three significant digits 6876 6874 544.5 321.5 6880 6870 545 322

Scientific Notation For extremely large or small numbers Powers of 10 Ex) Speed of light is 30,000,000,000 cm/s Move decimal to the left 10 spaces 30,000,000,000 cm/s 3 x 1010 cm/s Ex) Wavelength of yellow light is 0.000059 cm Move decimal to the right 5 spaces 0.000059 cm 5.9 x 10-5 cm

Scientific Notation Correct Scientific Notation: 5.20 x 104 Incorrect Scientific Notation: 520 x 102 Practice: Write in Scientific Notation. 6,200,000,000,000,000 6.2 x 1015 0.000000074 7.4 x 10-8

Significant Figures in Calculations Multiplication & Division Fewest significant digits 5.231 x 2.7 = 14 Addition & Subtraction Least precise 658.2 - 144 = 514

III. Unit Conversions SI Prefix Conversions 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 = _______ km 0.532 NUMBER UNIT NUMBER UNIT

A. SI Prefix Conversions Symbol Factor mega- M 106 kilo- k 103 deci- d 10-1 centi- c 10-2 move left move right milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12

A. SI Prefix Conversions 0.2 1) 20 cm = ______________ m 2) 0.032 A = ______________ mA 3) 45 m = ______________ nm 4) 805 dm = ______________ km 32 45,000 0.0805

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

B. 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.

B. 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

B. Dimensional Analysis Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? cm in 8 cm 1 in 2.54 cm = 3.15 in 

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

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 5K (5 km) race? km ft 5 km 1 mi 1.609 km 5280 ft 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 2.2. lb 1000 g 1 kg = 4545 g

B. Dimensional Analysis 8) Taft football needs 550 cm for a 1st down. How many yards is this? cm yd 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.01 yd