One of the common conversions we have to carry out in science is converting from degrees centigrade to degrees Fahrenheit.
The actual formula is: °F = (°C × 9/5) + 32 = (°C × 1.8) + 32
Lets try converting 30 °C to °F using this formula:
°F = (30 °C x 9/5) + 32 = (30 x 1.8) + 32 = 54 + 32 = 86
Now here is a simpler way, although it does not give the exact answer. But then we are often happy with “back-of-envelope” value, instead of an exact value. So here it is:
- Take the temperature in C, say 30 °C
- Double this temp, this gives 60 °C (so this is multiplying the original number by 2)
- Add 30. This gives 90 °F
So we can see this is fairly close to the exact value of 86.
So step 2 above (doubling) is because in the original formula we are multiplying C by 9/5 or by 1.8. We are using the rounded value of 1.8 as 2. Then in the original formula we have to add 32. In our approximation, we are adding only the rounded value 30.
This is an approximation. It is good enough for many situations. It works well for solving multiple choice questions (MCQs) in competitive exams.
How Accurate is this:
1. This trick is perfectly accurate at 10°C because 10°C x 2 + 30 = 50°F
2. Weather Range: Between 0°C and 30°C, the error is about 2-4° degrees. This level of error is acceptable. You can decide if you need a jacket. So, 20°C = 20 x 2 + 30 = 70°F. But actual conversion gives 20°C = 68°F. That gives an 2.9% error.
3. The further you get from 10°C, the less accurate it becomes. By our ‘trick calculation’, the boiling point of water at 100°C becomes 100 x 2 + 30 = 230°F. But the actual value is 212°F. That is an 8.5% error. So, use this trick with caution for higher temperatures.
Converting from Fahrenheit to Celsius:
The reverse calculation also works like this:
1. Take the temperature in F
2. Subtract 30 from this.
3. Divide by 2
Suppose it is 80°F. To go from Fahrenheit to Celsius:
1. Subtract 30 from °F: 80 – 30 = 50
2. Divide by 2: 50 / 2 = 25
So 80°F = 25°C
Actual answer is about 27°C so the error is small.
Do you know of other math hacks that you would like to share here? Please reply in the comment box below and we can make a post out of it!
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