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 all the problems: 1) Convert the length a) mm in 4.5 cm Step 1: Use the conversion factor 1 cm = 10 mm. Step 2: Multiply the given length by the conversion factor. 4.5 cm × 10 mm1 cm = 45 mm The length is 45 mm. b) mm in 60 cm Step 1: Use the conversion factor 1 cm = 10 mm. Step 2: Multiply the given length by the conversion factor. 60 cm × 10 mm1 cm = 600 mm The length is 600 mm. c) cm in 50 mm Step 1: Use the conversion factor 1 mm = 0.1 cm. Step 2: Multiply the given length by the conversion factor. 50 mm × 0.1 cm1 mm = 5 cm The length is 5 cm. d) cm in 25 mm (Assuming "cm in 25 cm" was a typo and meant "cm in 25 mm") Step 1: Use the conversion factor 1 mm = 0.1 cm. Step 2: Multiply the given length by the conversion factor. 25 mm × 0.1 cm1 mm = 2.5 cm The length is 2.5 cm. e) mm in 5000 cm Step 1: Use the conversion factor 1 cm = 10 mm. Step 2: Multiply the given length by the conversion factor. 5000 cm × 10 mm1 cm = 50000 mm The length is 50000 mm. f) mm in 8 km Step 1: Use the conversion factors 1 km = 1000 m and 1 m = 1000 mm. Step 2: Convert kilometers to meters, then meters to millimeters. 8 km × 1000 m1 km × 1000 mm1 m = 8000000 mm The length is 8000000 mm. g) mm in 0.65 km Step 1: Use the conversion factors 1 km = 1000 m and 1 m = 1000 mm. Step 2: Convert kilometers to meters, then meters to millimeters. 0.65 km × 1000 m1 km × 1000 mm1 m = 650000 mm The length is 650000 mm. 2) Convert the mass a) g in 2 kg Step 1: Use the conversion factor 1 kg = 1000 g. Step 2: Multiply the given mass by the conversion factor. 2 kg × 1000 g1 kg = 2000 g The mass is 2000 g. b) kg in 500 g Step 1: Use the conversion factor 1 g = 0.001 kg. Step 2: Multiply the given mass by the conversion factor. 500 g × 0.001 kg1 g = 0.5 kg The mass is 0.5 kg. c) kg in 2 Tonne Step 1: Use the conversion factor 1 Tonne = 1000 kg. Step 2: Multiply the given mass by the conversion factor. 2 Tonne × 1000 kg1 Tonne = 2000 kg The mass is 2000 kg. d) Tonne in 500 kg Step 1: Use the conversion factor 1 kg = 0.001 Tonne. Step 2: Multiply the given mass by the conversion factor. 500 kg × 0.001 Tonne1 kg = 0.5 Tonne The mass is 0.5 Tonne. e) g in 0.005 Tonne Step 1: Use the conversion factors 1 Tonne = 1000 kg and 1 kg = 1000 g. Step 2: Convert Tonne to kilograms, then kilograms to grams. 0.005 Tonne × 1000 kg1 Tonne × 1000 g1 kg = 5000 g The mass is 5000 g. 3) Convert the time a) min in 3/4 hrs Step 1: Use the conversion factor 1 hr = 60 min. Step 2: Multiply the given time by the conversion factor. (3)/(4) hrs × 60 min1 hr = 45 min The time is 45 min. b) min in 5 hrs Step 1: Use the conversion factor 1 hr = 60 min. Step 2: Multiply the given time by the conversion factor. 5 hrs × 60 min1 hr = 300 min The time is 300 min. c) hrs in 30 min Step 1: Use the conversion factor 1 min = (1)/(60) hr. Step 2: Multiply the given time by the conversion factor. 30 min × 1 hr60 min = 0.5 hrs The time is 0.5 hrs. d) hrs in 1800 min Step 1: Use the conversion factor 1 min = (1)/(60) hr. Step 2: Multiply the given time by the conversion factor. 1800 min × 1 hr60 min = 30 hrs The time is 30 hrs. e) sec in 3 min Step 1: Use the conversion factor 1 min = 60 sec. Step 2: Multiply the given time by the conversion factor. 3 min × 60 sec1 min = 180 sec The time is 180 sec. f) sec in 0.75 min Step 1: Use the conversion factor 1 min = 60 sec. Step 2: Multiply the given time by the conversion factor. 0.75 min × 60 sec1 min = 45 sec The time is 45 sec. g) sec in 0.005 hrs Step 1: Use the conversion factors 1 hr = 60 min and 1 min = 60 sec. Step 2: Convert hours to minutes, then minutes to seconds. 0.005 hrs × 60 min1 hr × 60 sec1 min = 18 sec The time is 18 sec. 4) Convert the capacity a) ml in 6 L Step 1: Use the conversion factor 1 L = 1000 ml. Step 2: Multiply the given capacity by the conversion factor. 6 L × 1000 ml1 L = 6000 ml The capacity is 6000 ml. b) ml in 0.25 L Step 1: Use the conversion factor 1 L = 1000 ml. Step 2: Multiply the given capacity by the conversion factor. 0.25 L × 1000 ml1 L = 250 ml The capacity is 250 ml. c) L in 300 ml Step 1: Use the conversion factor 1 ml = 0.001 L. Step 2: Multiply the given capacity by the conversion factor. 300 ml × 0.001 L1 ml = 0.3 L The capacity is 0.3 L. d) L in 4000 ml Step 1: Use the conversion factor 1 ml = 0.001 L. Step 2: Multiply the given capacity by the conversion factor. 4000 ml × 0.001 L1 ml = 4 L The capacity is 4 L. e) L in 2 kL Step 1: Use the conversion factor 1 kL = 1000 L. Step 2: Multiply the given capacity by the conversion factor. 2 kL × 1000 L1 kL = 2000 L The capacity is 2000 L. f) L in 0.0025 kL Step 1: Use the conversion factor 1 kL = 1000 L. Step 2: Multiply the given capacity by the conversion factor. 0.0025 kL × 1000 L1 kL = 2.5 L The capacity is 2.5 L. That's 2 down. 3 left today — send the next one.