Basic Units of Measurement and Conversions - Basic Mathematics for Water and Wastewater Operators - page 70

1. Add 40°.
2. Multiply by the appropriate fraction (5/9 or 9/5).
3. Subtract 40°.
Obviously, the only variable in this method is the choice of 5/9 or 9/5 in the multipli-
cation step. To make the proper choice, you must be familiar with the two scales. The
freezing point of water is 32° on the Fahrenheit scale and 0° on the Celsius scale. The
boiling point of water is 212° on the Fahrenheit scale and 100° on the Celsius scale.
Note: At the same temperature, higher numbers are associated with the Fahrenheit
scale and lower numbers with the Celsius scale. This important relationship helps
you decide whether to multiply by 5/9 or 9/5.
Now look at a few conversion problems to see how the three-step process works.
■ Example 2.133
Problem: Convert 200°F to Celsius.
Solution: Using the three-step process, we proceed as follows:
1. Add 40°:
200° + 40° = 240°
2. 240° must be multiplied by either 5/9 or 9/5. Because the conversion is to
the Celsius scale, we will be moving to a number smaller than 240. Through
reason and observation, obviously, if 240 were multiplied by 9/5, the result
would be almost the same as multiplying by 2, which would double 240
rather than make it smaller. If we multiply by 5/9, the result will be about
the same as multiplying by 1/2, which would cut 240 in half. Because in this
problem we wish to move to a smaller number, we should multiply by 5/9:
5/9 × 240° = 133.3°C
3. Now subtract 40°:
133.3°C - 40.0°C = 93.3°C
Therefore, 200°F = 93.3°C.
■ Example 2.134
Problem: Convert 24°C to Fahrenheit.
Solution: Using the three-step process, we proceed as follows:
1. Add 40°:
24° + 40° = 64°