This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the conversions for question 1a: i) 198 degrees to minutes Step 1: Use the conversion factor 1^ = 60'. 198^ = 198 × 60' Step 2: Calculate the product. 198 × 60 = 11880 The converted value is: 11880 minutes ii) 247 degrees, 30 minutes to seconds Step 1: Convert degrees to seconds using 1^ = 3600''. 247^ = 247 × 3600'' = 889200'' Step 2: Convert minutes to seconds using 1' = 60''. 30' = 30 × 60'' = 1800'' Step 3: Add the seconds together. 889200'' + 1800'' = 891000'' The converted value is: 891000 seconds iii) 2367 minutes to seconds Step 1: Use the conversion factor 1' = 60''. 2367' = 2367 × 60'' Step 2: Calculate the product. 2367 × 60 = 142020 The converted value is: 142020 seconds iv) 98.5 degrees to minutes Step 1: Use the conversion factor 1^ = 60'. 98.5^ = 98.5 × 60' Step 2: Calculate the product. 98.5 × 60 = 5910 The converted value is: 5910 minutes v) 6656 seconds to degree minutes seconds Step 1: Convert seconds to degrees by dividing by 3600''/degree. (6656)/(3600) = 1 with a remainder 1^ Step 2: Calculate the remaining seconds. 6656 - (1 × 3600) = 3056'' Step 3: Convert the remaining seconds to minutes by dividing by 60''/minute. (3056)/(60) = 50 with a remainder 50' Step 4: Calculate the remaining seconds. 3056 - (50 × 60) = 3056 - 3000 = 56'' The converted value is: 1 degree, 50 minutes, 56 seconds vi) 156 ft to meters Step 1: Use the conversion factor 1 ft = 0.3048 m. 156 ft = 156 × 0.3048 m Step 2: Calculate the product. 156 × 0.3048 = 47.5488 The converted value is: 47.5488 m vii) 708 meters to feet Step 1: Use the conversion factor 1 m = 3.28084 ft. 708 m = 708 × 3.28084 ft Step 2: Calculate the product. 708 × 3.28084 = 2322.83052 The converted value is: 2322.83052 ft viii) 1.23 km to meters Step 1: Use the conversion factor 1 km = 1000 m. 1.23 km = 1.23 × 1000 m Step 2: Calculate the product. 1.23 × 1000 = 1230 The converted value is: 1230 m ix) 100 ft to meters Step 1: Use the conversion factor 1 ft = 0.3048 m. 100 ft = 100 × 0.3048 m Step 2: Calculate the product. 100 × 0.3048 = 30.48 The converted value is: 30.48 m x) 0.55 km to meters Step 1: Use the conversion factor 1 km = 1000 m. 0.55 km = 0.55 × 1000 m Step 2: Calculate the product. 0.55 × 1000 = 550 The converted value is: 550 m