Proportional Reasoning-1
Unit conversions
Learn to change between units of length, area, weight and more.
You've already met the trap: a proportion means nothing if the two ratios use different units (2 kg against 200 g is really 2000 : 200). So a table of conversions is part of the toolkit.
| Quantity | Conversions |
|---|---|
| length | 1 metre = 3.281 feet |
| area | 1 square metre = 10.764 square feet; 1 acre = 43,560 square feet; 1 hectare = 10,000 square metres; 1 hectare = 2.471 acres |
| volume | 1 millilitre (mL) = 1 cubic centimetre (cc); 1 litre = 1,000 mL, or 1,000 cc |
Temperature is the awkward one, because the two scales don't start at the same place: 0 °C = 32 °F.
- Fahrenheit = (9/5) × Celsius + 32
- Celsius = (5/9) × (Fahrenheit − 32)
For instance 25 °C is (9/5) × 25 + 32 = 45 + 32 = 77 °F.
Notice that temperature is not a simple ratio: there's a '+ 32' in the way. That's the same lesson as the motorcycle: check that the relationship really is proportional before reaching for the Rule of Three.
Most conversions, though, are straightforward proportions, and they let you compare things measured in different systems. A farmer with a plot 200 ft by 500 ft has 1,00,000 square feet; at 43,560 square feet to the acre that's about 2.3 acres, so at 10 tonnes of manure per acre he needs about 23 tonnes.
The oldest problem in this chapter comes from the Lilavati. Weights were in palas and money in niskas: 'If 2½ palas of saffron costs 3/7 niskas, O expert businessman! Tell me quickly what quantity of saffron can be bought for 9 niskas?' Set it up as a Rule of Three and the fractions look worse than they are.
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