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Created by: Aramik Yousefian Presented by : Lilit Haroyan LAMC SSC Title V HSI Length Relations of U.S. and Metric Units • 1 in = 2.54 cm (exact) • 1 yd = 0.9144 m (exact) • 1 mi = 1.609 km Relations in U.S. units • 1 mi = 5280 ft • 1 mi = 1760 yd • 1 ft = 12 in So, 3 ft = 0.9144 m Mass Kilogram kg Relations of U.S. and Metric units • 1 lb = 0.4536 kg • 1 oz = 28.35 g Relations in U.S. units • 1 lb = 16 oz More Conversion Examples A cooler has a capacity of 5500 ml. What is the capacity in Liters? Ethyl alcohol has density of 0.79 g/ml. What is the volume in ml of 1.5kg of alcohol? 1L 5500 ml x 1000ml 1000 g 1.5 kg x 1 ml x 1 kg 1.2 L gas x = 1900 ml 0.79 g 1000 ml How many ml of olive oil (d=0.92g/ml) weigh the same as 1.2L of gasoline (d=0.66g/ml) = 5.5 L 0.66 g = 792 g gas x 1L 1 ml mass of olive oil = mass of gasoline = 792 g 1 ml 792 g oil x = 860 ml 0.92 g Put the decimal after the first digit. After the decimal place, there are 11 places left So, we drop the zeros and write… 1.23 x 10 11 Write 0.0000000000436 in scientific notation. 0.0000000000436 1 2 3 4 5 6 7 8 9 10 11 4.36 × 10–11 Convert 0.00000000578 to scientific notation. 0.00000000578 1 2 3 4 5 6 7 8 9 5.78 × 10–9 Ordinary Decimal Notation Scientific Notation 4000 5,720,000,000 –0.00036 0.00036 –36,000 4 x 103 5.72 x 109 –3.6 × 10–4 3.6 × 10–4 –3.6 × 104 • All non-zero digits are always significant. 123456789 • All zeros between two significant digits are always significant. 120450098014 • All zeros before the first non-zero digit are never significant. 0005520481004 • All zeros after the last non-zero digit and after the decimal are always significant. 1 2 0 0 0 0. 52.0000 • Trailing zeros before the decimal are ambiguous and therefore assumed to not be significant. 0055.00 0.0043 0.0035 2 sig figs 0.0035 0022005.0 6 sig figs 0022005.0 568000 3 sig figs 568000 0.003010 4 sig figs 0.003010 0,1,2,3 and 4 are always rounded down 5,6,7,8 and 9 are always rounded up Rounding Decimals 3.1416 rounded to hundredths is 3.14 1.2635 rounded to tenths is 1.3 1.2635 rounded to 3 decimal places is 1.264 Rounding whole Numbers 134.9 rounded to tens is 130 12,690 rounded to thousands is 13,000 1.239 rounded to units is 1 Significant digit calculations multiplication and division When multiplying or dividing numbers, the answer must contain the same number of significant figures as the measurement with the lowest number of significant figures. (1.353) x (0.12) = 1.6 addition and subtraction When adding or subtracting numbers, the answer must contain the same number of decimal places as the measurement with the lowest number of decimal places. (15.12) + (5.8) = 20.9 More Calculations 6.48 x 0.22 = 1.4256 1.4 0.006 + 5.24 = 5.246 5.25 8.06 = 2.7793103 2.8 2.9 (3.5) (4.544) = 5 3.1808 3 Percentage % 77 96 = 77% 100 = 96% 100 What is 35% of 68? X 35 100X X = 24 100 24 is 35% of 68. = = 68 (68)(35) 100 100 15 is what percentage of 80? 15 X 80X = 80 (15)(100) X = 19 80 19% of 80 is 15. = 100 80 your result - accepted value % error = X 100 accepted value Also written as experimental value - theoretical value % error = X 100 theoretical value % Error Example A student measures the volume of a 1.50 liter container to be 1.67 liters. What is the percent error in the student's measurement? Experimental Value: Theoretical value: 1.50 L 1.67 L 1.50 - 1.67 % error = X 1.67 - 0.17 X 1.67 100 = 100 10% error