In my last post I quipped about how difficult it was to get used to get used to the WMUs (Weird Measurement Units) here in the US. Well, as the winter sets in, as so does the curiosity to check the weather every time I step out. Back in my country and in UK, temperatures are reported in Degree Celsius, however, every one here seems to speak the Farenheit language. Most apps and online weather channels do provide both formats, but it gets tricky when you are talking to someone or listening to the radio on a bus. The other day, temperature read 5 degree Farenheit, but no one mentions the F at the end of the number and for someone like me it really gets difficult to realize how cold the weather is without actually converting to Celsius. In this case it was a shivering 15 degree below freezing.
So, I wanted a quick and easy way to make these conversions, not having to pull up a calculator every time. Here it goes, this is an approximate conversion and has an 'acceptable' error. The actual from F to C is (F-32)*5/9. My approximation is simple, subtract 30 from F and divide the result by 2 to get the Celsius value. In other words, just do (F-30)/2 to get C. The trick works because you are increasing both numerator and the denominator to make the approximation. Lets take a few examples and see what the error would look like. For a temperature of 70F, the actual conversion would give 21.1 C, whereas this quick method will give 20 C, which is fairly close to get a sense of what the weather is like. The error is higher for lower values but still within reasonable limits. For example for 5F the actual conversion gives -15 C whereas the approximation yields -12.5 C. The reason why I call this approximation technique acceptable is for two reasons, one, we do not need an accurate values of temperature to know how the weather is like, we don't see much difference in the way we will dress up if the weather was say 12 or 15 degree Celsius. Second the range of temperature readings across all weather conditions is fairly small, at worst from -30 F to 110 F.
It does not stop there, for me to make sense of most things, I needed to employ such techniques to other types of measurements. The most prominent one was to weigh stuff in pounds instead of kilograms. I did not take this too seriously since I would always just assume that one kg is almost twice as heavy as one pound. However, this naive approach does not always work very well, it works fine for stuff like groceries, but its highly error prone for something like weighing yourself or knowing how much you have been lifting at the gym in lifting weights. For example if someone weighed 154 pounds then according to my naive approach that person should weigh 77 Kilograms but the correct conversion would give about 70 Kilograms. This is a huge difference if I have to interpret how much someone weighs.
So to overcome this here is a simple technique. The error is because we are over estimating and need a negative correction. So after we divide the value in pounds by 2, we subtract the resulting value by one tenth of the resulting value. So in the above example, we first divide 154 by 2 which gives 77 and then subtract 7.7 (approximate to 8) from 77 which gives 69. This has been a useful technique especially when lifting weights in the gym. Since all my life I have been used to seeing plates and dumbbells in kilograms, it made me difficult to estimate how much weight I could lift.
Things are much better when it comes to the most common measuring unit in grocery stores, what I call the 'omnipresent ounce'. The correct conversion of ounce to grams is my multiplying the value with 28.3, which is almost impossible for a human calculator. Hence, I have the following approximation. Multiply the value in ounce by 30 and subtract the resulting value G by one tenth (T) of the resulting value. To getter a better approximation, add half of the computed one tenth (T/2) to G. Instead of the two step process, you could just subtract by one twentieth of G. For example if we have to convert 5 ounces in grams, the correct conversion gives 142 grams. To convert this using the above technique first, multiply 5 by 30 which gives 150. We next have to find one twentieth of 150, to do this, we first compute one tenth of 150 which is 15. One twentieth is half of this computed value which gives 7.5. Now subtract 7.5 from 150 which gives 142.5, very close to the actual value. The approximation really works extremely well since in practice the maximum of value of an item in ounces may never exceed say 64 ounces. This is where the significance of measuring in ounce becomes relevant, because it is extremely convenient to use ounce for items that are less than a pound and not more than a few pounds. Every pound has exactly 16 ounces and therefore makes it convenient to use ounce to get a fine grained measure without having to use real numbers.
There are a few more like Gallons to liters and miles to kilometers, while these conversions may not have as much significance in everyday use, nevertheless, they are also fairly straightforward to make approximate calculations. A gallon can be easily converted to liters by just multiplying by 4, and one mile is approximately one and a half times a kilometer. I have personally not see the need to make these conversions since it is very easy to get accustomed to these units that the ones mentioned above.
I anticipated this to be a very short blog, but it has turned out to be, well, not so short and hopefully not so boring. It makes me wonder, why is it that no one has blogged about this, since I did observe fair bit of cultural difference in the way people communicated in their own language of measurement.
So, I wanted a quick and easy way to make these conversions, not having to pull up a calculator every time. Here it goes, this is an approximate conversion and has an 'acceptable' error. The actual from F to C is (F-32)*5/9. My approximation is simple, subtract 30 from F and divide the result by 2 to get the Celsius value. In other words, just do (F-30)/2 to get C. The trick works because you are increasing both numerator and the denominator to make the approximation. Lets take a few examples and see what the error would look like. For a temperature of 70F, the actual conversion would give 21.1 C, whereas this quick method will give 20 C, which is fairly close to get a sense of what the weather is like. The error is higher for lower values but still within reasonable limits. For example for 5F the actual conversion gives -15 C whereas the approximation yields -12.5 C. The reason why I call this approximation technique acceptable is for two reasons, one, we do not need an accurate values of temperature to know how the weather is like, we don't see much difference in the way we will dress up if the weather was say 12 or 15 degree Celsius. Second the range of temperature readings across all weather conditions is fairly small, at worst from -30 F to 110 F.
It does not stop there, for me to make sense of most things, I needed to employ such techniques to other types of measurements. The most prominent one was to weigh stuff in pounds instead of kilograms. I did not take this too seriously since I would always just assume that one kg is almost twice as heavy as one pound. However, this naive approach does not always work very well, it works fine for stuff like groceries, but its highly error prone for something like weighing yourself or knowing how much you have been lifting at the gym in lifting weights. For example if someone weighed 154 pounds then according to my naive approach that person should weigh 77 Kilograms but the correct conversion would give about 70 Kilograms. This is a huge difference if I have to interpret how much someone weighs.
So to overcome this here is a simple technique. The error is because we are over estimating and need a negative correction. So after we divide the value in pounds by 2, we subtract the resulting value by one tenth of the resulting value. So in the above example, we first divide 154 by 2 which gives 77 and then subtract 7.7 (approximate to 8) from 77 which gives 69. This has been a useful technique especially when lifting weights in the gym. Since all my life I have been used to seeing plates and dumbbells in kilograms, it made me difficult to estimate how much weight I could lift.
Things are much better when it comes to the most common measuring unit in grocery stores, what I call the 'omnipresent ounce'. The correct conversion of ounce to grams is my multiplying the value with 28.3, which is almost impossible for a human calculator. Hence, I have the following approximation. Multiply the value in ounce by 30 and subtract the resulting value G by one tenth (T) of the resulting value. To getter a better approximation, add half of the computed one tenth (T/2) to G. Instead of the two step process, you could just subtract by one twentieth of G. For example if we have to convert 5 ounces in grams, the correct conversion gives 142 grams. To convert this using the above technique first, multiply 5 by 30 which gives 150. We next have to find one twentieth of 150, to do this, we first compute one tenth of 150 which is 15. One twentieth is half of this computed value which gives 7.5. Now subtract 7.5 from 150 which gives 142.5, very close to the actual value. The approximation really works extremely well since in practice the maximum of value of an item in ounces may never exceed say 64 ounces. This is where the significance of measuring in ounce becomes relevant, because it is extremely convenient to use ounce for items that are less than a pound and not more than a few pounds. Every pound has exactly 16 ounces and therefore makes it convenient to use ounce to get a fine grained measure without having to use real numbers.
There are a few more like Gallons to liters and miles to kilometers, while these conversions may not have as much significance in everyday use, nevertheless, they are also fairly straightforward to make approximate calculations. A gallon can be easily converted to liters by just multiplying by 4, and one mile is approximately one and a half times a kilometer. I have personally not see the need to make these conversions since it is very easy to get accustomed to these units that the ones mentioned above.
I anticipated this to be a very short blog, but it has turned out to be, well, not so short and hopefully not so boring. It makes me wonder, why is it that no one has blogged about this, since I did observe fair bit of cultural difference in the way people communicated in their own language of measurement.
