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Working with Units

Working with Units. Math makes sense. What’s the Point?. Units identify the type of quantity Units give meaning to measurements. Eat a live bullfrog first thing in the morning…. …and nothing worse will happen to you for the rest of the day!. 6 x. = 3 x / y. 2 y. 6 C. = 3 C/s.

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Working with Units

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  1. Working with Units Math makes sense

  2. What’s the Point? • Units identify the type of quantity • Units give meaning to measurements

  3. Eat a live bullfrog first thing in the morning… …and nothing worse will happen to you for the rest of the day!

  4. 6 x = 3 x/y 2 y 6 C = 3 C/s 2 s Do math with units • Unit labels can be treated like any variable in algebra. Add them! 3 x + 4 x = 7 x 3 s + 4 s = 7 s Divide them! Multiply them! (3a)(4b) = 12 ab (3 m/s)(4 s) = 12 m

  5. Compound Units • Areas • Volumes • Accumulated effects • Effects of population Represent:

  6. Compound Units a Area = ab b

  7. Compound Units Effort = (3 w) (4 h) = 12 (w)(h) = 12 worker·hours 3workers 4 h

  8. Ratio Units • Rates of change • Intrinsic properties Represent:

  9. 10 0.75 y 8 mass (kg) 6 5.4 kg 5.4 kg 4 0.75 y 2 0 0 1 time (y) Ratio Units A baby has a mass of 3.2 kg at birth and 8.6 kg 9 months later. What is its average annual growth rate during this time? slope = = 7.2 kg/y

  10. 39.37 in 1 m 1 = 1 = 1 m 39.37 in 72 = m 39.37 1 m = 72 in · 39.37 in Manipulating Units • Conversions 39.37 in = 1 m equality conversion factors 72 in = 72 in · 1 = 1.829 m

  11. Group Work • 1 mi = 5280 ft1 yd = 3 ft Set up the conversion 2 mi to yd. • 1 mi = 5280 ft1 ft = 12 in1 m = 39.37 in1 h = 3600 sSet up the conversion 75 mi/h to m/s.

  12. Reading for Next Time • Distance, velocity, and acceleration: how physics describes motion • Keep in mind the relations between different quantities

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