8th Edition: Homework Assignment #1: problems: 1,7,9,11,13,14,27, 29, and 30. 1. Express each of the following numbers in scientific notation: (scientific notation has only one digit to the left of the decimal point – the power of ten exponent can be of any value) a. 3000 b. 75,000 c. 2,000,000 3.0 x103 7.5 x104 2 x106 7. Express each of the following as a regular decimal number: (Remember if the exponent sign is “+” move the decimal point to the right and if it is “-“ move the decimal point to the left.) a. b. c. 2.5 x10-6 5.0 x102 3.9 x10-1 0.0000025 500 0.39 9. Add the following numbers: (exponents must be the same value – adjust one of the numbers to make it the same as the other.) a. (9.2 x106) + (3.4 x107) = (0.92 x107) + (3.4 x107) = 4.32 x107 I have found that converting the value that has the smaller exponent value to match the larger value keeps the numbers more manageable. b. (5 x103) + (8.5 x10-1) = (5 x103) + (0.00085 x103) = 5.00085 x103 c. (5.6 x10-8) + (4.6 x10-9) = (5.6 x10-8) + (0.46 x10-8) = 6.06 x10-8 11. Perform the following multiplications: (exponents are added to perform multiplication) a. (5 x103)(4 x105) = (5 x 4) x103+5 = 20 x108 b. (1.2 x1012)(3 x102) = (1.2 x 3) x1012+2 = 3.6 x1014 c. (2.2 x 10-9)(7 x10-6) = (2.2 x 7) x10-9+-6 = 15.4 x 10-15 = 1.54 x 10-14 13. Express each of the following numbers in Engineering Notation: (number to the left of the decimal has to be between 1 and 999, with the exponent being a multiple of 3. Remember to put power of ten notation into Metric prefixes) a. 89,000 = 89,000 x100 = 89 x103 = 89k b. 450,000 = 450,000 x100 = 450 x103 = 450k c. 12,040,000,000,000 = 12,040,000,000,000 x100 = 12.04 x1012 = 12.04T 14. Express each of the following in engineering notation: a. 2.35 x105 = 23.5 x104 = 235 x103 = 235k b. 7.32 x107 = 73.2 x106 = 73.2M c. 1.333 x109 = 1.333G (already in proper form) 27. Perform the indicated conversions: (First convert the prefix into power of ten notation then if going from a larger exponent to a smaller one move the decimal to the right; going from a smaller exponent to a larger one move the decimal to the left.) a. 5mA to microamperes ≈ 5 x10-3A = 5000 x10-6A =5000μA b. 3200μW to milliwatts ≈ 3200 x10-6W = 3.2 x10-3W = 3.2mW c. 5000kV to Megavolts ≈ 5000 x103V = 5 x106V = 5MV d. 10MW to kilowatts ≈ 10 x106W = 10,000 x103W = 10,000kW 29. Add the following quantities: (First convert the prefixes into power of ten notation; adjust so exponents are equal then add) a. 50mA + 680 μA ≈ 50 x10-3A + 680 x10-6A = 50 x10-3A + 0.680 x 10-3A = 50.68 x10-3A = 50.68mA (see calculator application) b. 120kΩ + 2.2MΩ ≈ 120 x103Ω + 2.2 x106Ω = 0.12 x106Ω + 2.2 x106Ω = 2.32 x106Ω = 2.32MΩ (see calculator application) c. 0.02μF + 3300pF ≈ 0.02 x10-6F + 3300 x10-12F = 0.02 x10-6F + 0.0033 x10-6F = 0.0233 x10-6F = 23.3 x 10-9 = 23.3nF (see calculator application) 30. Do the following operations: (convert metric prefixes into power of ten format; note the use of parentheses to keep order of math operations) a. 10kΩ / (2.2 kΩ + 10 kΩ) 10k Ω 10 × 103 Ω 10 × 103 Ω ⇒ = = 0.8196721= × 103−3 Ω 0.8196721 = × 100 Ω 819.67= × 10 −3 Ω 819.67m Ω (2.2k Ω + 10K Ω) (2.2 × 103 Ω + 10 × 103 Ω) 12.2 × 103 Ω (see calculator application) b. 250mV / 50μV 250mV 250 × 10 −3V 250 5 × 10 −3+6V = 5 × 103V = 5kV ⇒ ⇒ × 10( −3) −( −6)V = −6 50 µV 50 × 10 V 50 (see calculator application) c. 1MW / 2KW 1MW 1 × 106W 1 ⇒ ⇒ × 106 −3W = 0.5 × 103W = 500W 3 2kW 2 × 10 W 2 (see calculator application)