A. Basics of quantities and precision1. Convert each of the following to the appropriate SI unit, with appropriatesignificant digits, and with appropriate use of scientific notation. Note: alwaysuse 365.25 days per year (10 marks):a) 0.00014000 years:b) 0.002560000000000007 tonnes:c) 1.369 nm:d) 140,000,000 Mg/km3:e) 0.0009450 m2:2. How many significant digits are in each of the following values? (5 marks)a) 0.0007600b) 1.7890c) 0.000000000101d) 0.0000000001010e) 5.67*1062 of 43. Answer the following arithmetic questions, with a final response in the correctSI units (where necessary). Use scientific notation where appropriate only. (14marks)a) 124.1 g + 35.678 mg =b) 124.16 km 350.7 m =c) 23.1 m2+ 345.65 ha =d) 5600.023 cm3£ 6 cm2=e) 100 W m-2x 4.56 J s-1m-2 23.567 W m-2=f) 1.02x106km2£ 1.02x106km2=g) (236589 dm + 441911 dm) £ 1.00 years =4. If the surface area of the earth is 510,100,000 km2what is the radius of theearth (in metres)? (Assume: the earth is a sphere, the surface area of a sphere is4pr2, and p = 3.14). If you were able to travel this distance in 6.15 days, howfast would your average speed be (in km h-1)? (5 marks)3 of 4B. Understanding units in hydrologic and soil science problem solving (20 marks):Provide answers to the following problems. Show all of your work and remembersignificant figures. If there are units you are unfamiliar with, look them up (yourpractical guidebook is a particularly good resource). EACH QUESTION = 4MARKS.1. Rain falls onto a 4.0 km2watershed at a rate of 2 mm hr-1, for a total of 11.5hours. If water is known to be 1000 L m-3, how many litres of rain fell on thewatershed during the entire rainstorm?2. If Highland Creek flows out of its watershed (same area as above) at a rate of 4.37x 10-7km3hr-1, what is the total runoff (in mm) over 1.167 days?3. Soil erodes away from a farmers field at a rate of 13.67 metric tonnes ha-1yr-1.In 3.05 years, how much soil (in kg) will have eroded from 4.61 acres? 4 of 44. If this same soil were 68.92 cm thick and with a density of 1.25 g cm-3, how longwould it take to erode away the entire 4.61 acres?5. Water is vapourized and blown into a balloon until the total balloon volume is 568cubic inches. A total of 2.09 L of water vapour was blown in. Presumingeverything is at standard pressure and temperature, 1000 L of water has a mass of1 metric tonne. What is the density of water vapour in the balloon in units of kgm-3? If the density of water at saturation vapour pressure under these conditionsis 3 x 102kg m-3, what is the relative humidity (%) within the balloon?; A. Basics of quantities and precision1. Convert each of the following to the appropriate SI unit, with appropriatesignificant digits, and with appropriate use of scientific notation. Note: alwaysuse 365.25 days per year (10 marks):a) 0.00014000 years:b) 0.002560000000000007 tonnes:c) 1.369 nm:d) 140,000,000 Mg/km3:e) 0.0009450 m2:2. How many significant digits are in each of the following values? (5 marks)a) 0.0007600b) 1.7890c) 0.000000000101d) 0.0000000001010e) 5.67*1062 of 43. Answer the following arithmetic questions, with a final response in the correctSI units (where necessary). Use scientific notation where appropriate only. (14marks)a) 124.1 g + 35.678 mg =b) 124.16 km 350.7 m =c) 23.1 m2+ 345.65 ha =d) 5600.023 cm3£ 6 cm2=e) 100 W m-2x 4.56 J s-1m-2 23.567 W m-2=f) 1.02x106km2£ 1.02x106km2=g) (236589 dm + 441911 dm) £ 1.00 years =4. If the surface area of the earth is 510,100,000 km2what is the radius of theearth (in metres)? (Assume: the earth is a sphere, the surface area of a sphere is4pr2, and p = 3.14). If you were able to travel this distance in 6.15 days, howfast would your average speed be (in km h-1)? (5 marks)3 of 4B. Understanding units in hydrologic and soil science problem solving (20 marks):Provide answers to the following problems. Show all of your work and remembersignificant figures. If there are units you are unfamiliar with, look them up (yourpractical guidebook is a particularly good resource). EACH QUESTION = 4MARKS.1. Rain falls onto a 4.0 km2watershed at a rate of 2 mm hr-1, for a total of 11.5hours. If water is known to be 1000 L m-3, how many litres of rain fell on thewatershed during the entire rainstorm?2. If Highland Creek flows out of its watershed (same area as above) at a rate of 4.37x 10-7km3hr-1, what is the total runoff (in mm) over 1.167 days?3. Soil erodes away from a farmers field at a rate of 13.67 metric tonnes ha-1yr-1.In 3.05 years, how much soil (in kg) will have eroded from 4.61 acres? 4 of 44. If this same soil were 68.92 cm thick and with a density of 1.25 g cm-3, how longwould it take to erode away the entire 4.61 acres?5. Water is vapourized and blown into a balloon until the total balloon volume is 568cubic inches. A total of 2.09 L of water vapour was blown in. Presumingeverything is at standard pressure and temperature, 1000 L of water has a mass of1 metric tonne. What is the density of water vapour in the balloon in units of kgm-3? If the density of water at saturation vapour pressure under these conditionsis 3 x 102kg m-3, what is the relative humidity (%) within the balloon?
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