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Cadiz 13-14 Physics Name _________________________ Date ______________Section ______ Extra Practice Units Calculations and Math Operations Work problems that you may have difficulty with first. Dimension Length Volume Mass Temperature Time Unit Symbol Quantities of each unit are related by powers of 10. Prefixes tell you how the units are related. Write the symbol and meaning of the prefixes below: Prefix giga Mega kilo hecto deka deci centi milli micro nano 1. 2. 3. 4. 5. 6. 7. 8. 1. Symbol How many in a unit 1g= _____ kg 1 kg = _____ g 1 m = _____ km 1 km = _____ m 1 m = _____ cm 1 cm = _____ m 1 L = _____ mL 1 mL = _____ L If you need to multiply or divide numbers, the number of significant figures in the answer must be the same as the number of significant figures in the measurement with the least significant figures. For example: 5.61 x 2.0 = 11. Try: a. 35.78 / 4.4 b. 105 x 3.4 c. 6.798 x 9.25 2. Meaning d. e. f. 4.27 / 5.5 6.789 x 1.0 5.0 / 1.546 If you need to add or subtract numbers, the number of decimal places in the answer cannot be greater than the least number of decimal places in the measurements. For example: 1.536 + 2.0 = 3.5. Try: a. b. c. d. e. f. 4.5 + 8.99 0.004 + 0.1 49 + 1.1 99.5 – 1.4 224.44 – 1.678 97.34 – 55.1 1. Express the following in scientific notation: a. 50,000 grains of sand = b. 0.00006 mm = c. (7.6 x 10-4m) x (1.5 x 107m) = d. 0.00053 / 29 = e. How far does light travel in 8.64 x 104 seconds (speed of light is 3.0 x 108m/s) 2. How many significant figures are in 14.99876? 3. 4. Calculate 43.5 + 6.779 = Calculate 43.5 x 6.779 = What is the density of a brick with mass 45.9 g and volume of 34.56 cubic centimeters? 5. Convert 46 degrees Fahrenheit into Celsius. 6. Compare the temperature of the human body in degrees Fahrenheit and Celsius. Scientific notation presents an easier way to write very large and very small numbers. Instead of writing 67,000,000,000, we use a power notation. We write 6.7 x 10 10. 6.7 is the coefficient – always a number between 1 and 10. 10 is the base. The superscript 10 means that the decimal point is 10 spots to the right. Instead of writing 0.00000000056, we write 5.6 x 10 -10. The superscript -10 means that the decimal point is 10 spots to the left. Complete the following: Number 45,000 378,000 6,890,000 0.05 0.0089 0.00071 Scientific notation 5.6 x 109 3.25 x 106 1.322 x 103 1.4 x 10-5 9.24 x 10-8 7. A mountain’s elevation above sea level is 9.8 x 10 3 m. Write the elevation in standard notation 8. The eye’s retina contains about 130 million light-sensitive cells. How many is that in scientific notation? 9. A mulberry silkworm can spin a single thread that measures up to 1300 m in length. How long it that in scientific notation? Multiplying and Dividing: When you multiply in scientific notation, you multiply the coefficients and add the exponents. For example, (1.1 x 10 3) x (5.1 x 104) = 5.6 x 107. When you divide in scientific notation, you divide the coefficients and subtract the exponents. For example, (5.1 x 10 6) / (1.1 x 103) = (4.6 x 103). If the coefficient of your answer is not between 1 and 10, you need to alter it to be in scientific notation. Try the following: 1. (4.7 x 105) x (2.1 x 104) = 2. (3.2 x 104) x (3.2 x 107) = 3. (5.6 x 10-4) x (1.3 x 10-5) = 4. (8.7 x 103) x (5.1 x 104) = 5. (6.4 x 109) / (2.0 x 104) = 6. (9.1 x 103) / (3.2 x 106) = 7. (8.4 x 10-3) / (9.8 x 10-2) = 8. (1.3 x 10-9) / (3.4 x 10-11) = 9. A rectangular lake has a width of 6000 m and a length of 1.2 x 10 4 m. What is the area of the lake in scientific notation? 10. One surface of a cut gemstone is rectangular in shape. It is 0.0002 m wide and has an area of 0.000006 m2. How long is the surface in scientific notation? Adding and Subtracting: When you add or subtract in scientific notation, the coefficients must be raised to the same power of 10. If they are not, convert them first. Add the coefficients together and keep the same exponent. If the coefficient of your answer is not between 1 and 10, you need to alter it to be in scientific notation. Try the following: 1. 2. 3. 4. (1.3 x 104) + (4.4 x 104) = (6.2 x 105) – (1.5 x 105) = (9.8 x 106) – (8.9 x 105) = (5.6 x 107) – (4.4 x 108) = Convert the following> You MUST use units and factor label format taught in class 1. 35dm to meters 2. 4 hours to seconds 3. 4 hours to days. 4. 4 hours to years 5. 55 miles per hour to meters per second 6. 2.5 tons per year to grams per second 7. 5 Liters per second to gallons per minute