UNITS Science makes all measurements using the metric system Length Meter (m) Mass Gram (g) Volume Liter (L) ( = 39.37 inches) ( = 0.035274 ounces) ( = 1.060 quarts) EX1-1 (of 29)

Prefix Symbol Base Unit Multiplying Factor giga G 109 mega M 106 METRIC PREFIXES Prefix Symbol Base Unit Multiplying Factor giga G 109 mega M 106 kilo k 103 BASE UNIT 100 Yippe-kai-ay, BUMF 1 byte = bytes 1 m = m 1 g = g John McClane EX1-2 (of 28)

METRIC PREFIXES Prefix Symbol Base Unit Multiplying Factor giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 EX1-3 (of 28)

Convert 525 meters into kilometers An EQUALITY STATEMENT between meters and kilometers is needed 1 BIG km = 103 small m ____ 100 1 km = 103 m METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 larger unit  EX1-4 (of 28)

Convert 525 meters into kilometers An equality statement can be written as a fraction called a CONVERSION FACTOR METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 103 m _______ 1 km 1 km _______ 103 m or 525 m x 1 km ________ 103 m = 0.525 km EX1-5 (of 28)

Convert 0.170 grams into centigrams 1 BIG g = 100 small cg _____ 10-2 1 g = 102 cg METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 0.170 g x 102 cg ________ 1 g = 17.0 cg larger unit  EX1-6 (of 28)

Convert 24.5 milliliters into liters 1 BIG L = 100 small mL _____ 10-3 1 L = 103 mL METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 24.5 mL x 1 L ________ 103 mL = 0.0245 L larger unit  EX1-7 (of 28)

Convert 0.674 decimeters into micrometers 1 BIG dm = 10-1 small μm _____ 10-6 1 dm = 105 μm METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 0.674 dm x 105 μm _________ 1 dm = 67,400 μm larger unit  EX1-8 (of 28)

Convert 22.5 mL/s into L/min 1 BIG L = 103 small mL 1 min = 60 s METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 22.5 mL ___________ s x 1 L ________ 103 mL x 60 s ________ 1 min = 1.35 L/min EX1-9 (of 28)

Convert 187.0 J/hr into kJ/day 1 BIG kJ = 103 small J 1 day = 24 hr METRIC PREFIXES Prefix Symbol BUMF giga G 109 mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 187.0 J __________ hr x 1 kJ _______ 103 J x 24 hr ________ 1 day = 4.488 kJ/day EX1-10 (of 28)

Tolerances: the expected variation MEASUREMENTS All measurements contain error because the last bit of each measurement must be estimated 6.8 cm ± 0.1 cm 6.80 cm ± 0.01 cm TOLERANCE – For a piece of equipment, it is the expected range of variation in a reading Tolerances: the expected variation for each ruler EX1-11 (of 28)

MEASUREMENTS All measurements contain error because the last bit of each measurement must be estimated 6.8 cm 6.7 to 6.9 cm 6.80 cm 6.79 to 6.81 cm TOLERANCE – For a piece of equipment, it is the expected range of variation in a reading Expected range for the measured value EX1-12 (of 28)

TOLERANCES OF GRADUATED EQUIPMENT Tolerances are usually larger than ±1 in the last decimal place Tolerances are often provided by the manufacturer 5-mL Volumetric Pipet : ± 0.02 mL 50-mL Volumetric Buret : ± 0.03 mL 100-mL Volumetric Flask : ± 0.08 mL A tolerance in the hundredths place means the measurement should be given to the hundredths place Reading for a 5-mL Volumetric Pipet : 5.00 mL Expected range for the measured value : 4.98 mL to 5.02 mL 5.00 ± 0.02 mL EX1-13 (of 28)

SIGNIFICANT FIGURES Provide a method to insure answers to arithmetic operations with measurements maintain the same tolerance SIGNIFICANT FIGURES – Every digit recorded in a measurement (all certain digits plus one uncertain digit) EX1-14 (of 28)

from the least reliable measuring device 59 cm 59.6 cm 59.63 cm 59 cm 59.6 cm 59.63 cm 58 to 60 cm 59.5 to 59.7 cm 59.62 to 59.64 cm 2 sig fig’s 3 sig fig’s 4 sig fig’s from the least reliable measuring device from the most reliable measuring device EX1-15 (of 28)

Significant figures are determined only for measurements , not for (1) Counted numbers (28 students enrolled) (2) Defined numbers (1 km = 103 m) EX1-16 (of 28)

RULES FOR COUNTING SIGNIFICANT FIGURES (1) The first significant figure in a measurement is the first non-zero digit 24.75 3,041 0.0876 4 4 3 24.74 to 24.76 3,040 to 3,042 0.0875 to 0.0877 EX1-17 (of 28)

RULES FOR COUNTING SIGNIFICANT FIGURES (2) Zeros that end a number with a decimal point are significant 37.0 0.70 0.0430 250. 3 2 3 3 (3) Zeros that end a number without a decimal point are not significant 500 270 1 2 EX1-18 (of 28)

A non-significant zero can be made significant with a bar over it 300 _ 300 _ 300 300.0 1 2 3 4 200 to 400 290 to 310 299 to 301 299.9 to 300.1 EX1-19 (of 28)

12.3 12.370 0.00524 0.0010 3 5 3 2 600 23.00 3,019 43,100 1 4 4 3 1,600. 0.00313 19.027 0.07204 4 3 5 4 EX1-20 (of 28)

When writing a measurement in scientific notation, only significant figures are shown _ 680 680 680.0 6.8 × 102 6.80 × 102 6.800 × 102 EX1-21 (of 28)

ADDING AND SUBTRACTING MEASUREMENTS Approximate technique – The answer’s last digit will be in the same place as the last digit in the least accurate addend 20.63 mL + 6.6 mL Last sig fig: hundredths place Last sig fig: tenths place 27.23 mL 27.2 mL Last sig fig must be in the tenths place ← Correct answer EX1-22 (of 28)

ADDING AND SUBTRACTING MEASUREMENTS Approximate technique – The answer’s last digit will be in the same place as the last digit in the least accurate addend 1,840 km + 576 km Last sig fig: tens place Last sig fig: ones place 2,416 km 2,420 km Last sig fig must be in the tens place ← Correct answer EX1-23 (of 28)

ADDING AND SUBTRACTING MEASUREMENTS Exact technique – The answer’s tolerance is the sum of the tolerances of each measurement 24.53 ± 0.05 g 0.784 ± 0.002 g + 9.6172 ± 0.0001 g 24.9312 ± 0.0521 g ← Give the tolerance to only one digit 24.93 g ± 0.05 ← Last sig fig must match the tolerance EX1-24 (of 28)

MULTIPLYING AND DIVIDING MEASUREMENTS Approximate technique – The number of sig fig’s in the answer will equal the number of sig fig’s in the factor with the least number of sig fig’s (2.41 m)(0.25 m) = 0.6025 m2 Answer = 0.60 m2 Sig Fig’s: 3 2 Answer will have 2 sig fig’s EX1-25 (of 28)

MULTIPLYING AND DIVIDING MEASUREMENTS Approximate technique – The number of sig fig’s in the answer will equal the number of sig fig’s in the factor with the least number of sig fig’s 617.4 m ÷ 0.50 s = 1,234.8 m/s Answer = 1,200 m/s Sig Fig’s: 4 2 Answer will have 2 sig fig’s EX1-26 (of 28)

MULTIPLYING AND DIVIDING MEASUREMENTS Exact technique – The answer’s RELATIVE tolerance is the sum of the RELATIVE tolerances of each measurement (0.313 ± 0.002 L)(44.30 ± 0.03 atm) ____________________________________________ (1.1233 ± 0.0005 L) = 12.3439 atm 0.002 = 0.00639 ________ 0.313 0.03 = 0.000677 ________ 44.30 0.0005 = 0.000445 _________ 1.1233 0.00639 + 0.000677 + 0.000445 = 0.007512 EX1-27 (of 28)

MULTIPLYING AND DIVIDING MEASUREMENTS Exact technique – The answer’s RELATIVE tolerance is the sum of the RELATIVE tolerances of each measurement (0.313 ± 0.002 L)(44.30 ± 0.03 atm) ____________________________________________ (1.1233 ± 0.0005 L) = 12.3439 atm Relative tolerance for answer = 0.007512 Actual tolerance for the answer = (answer)(relative tolerance) = (0.007512)(12.3439) = 0.0927 = 0.09 Answer = 12.34 ± 0.09 atm EX1-28 (of 28)