## Teachers Love Unit Conversion Problems

Unit conversion is a popular feature in both math and physics problems. Afterall, living in the world with various dimension systems (metric and imperial being only two examples) means that students should be aware of the need for converting pounds to kilograms, degrees Fahrenheit to degrees Celsius, miles to kilometers, and, of course, dollars to euro. Here we'll focus on pounds and kilograms.

## A Coarse Approximation

With this in mind, the logical questions to follow are how to convert pounds to kilograms and how to convert kilograms to pounds. A very easy-to-remember (and fairly accurate) approximation when talking about converting kilograms to pounds is that weight in pounds is twice the weight in kilograms. So, roughly, 200 pounds is 100 kilograms, 2,000 pounds is a ton (a thousand kilos) and 50 kilograms is 100 pounds. This approximation of unit conversion is only good, however, when you need a general idea of someone’s or something’s weight or mass.

## The Definition

Introduced in 1959 in the USA and in 1963 in the UK, it is stated that one pound ”shall be 0.45359237 kilogram, exactly”. This means one

kilogram is approximately 2.20462262 pounds. Of course, for most practical purposes, the second decimal digit is acceptable accuracy, so we should mostly use 1kg = 2.2lb; 1lb = 0.45kg, or 1lb = 0.453 kg. Note that both of those approximations are slightly underrated (actually, the pound is slightly more than 0.45kg, and a kilogram is slightly more than 2.2 pounds).

## Sample Problem

Consider this question: John, living in Toronto comes to visit his friend Jane in Buffalo. John knows his weight is 66 kilograms. Jane had read research stating that for her height of 5 feet, the ideal weight would be by 1.5 times lower than John’s. How many pounds does Jane need to lose if her current weight is 110 pounds?

We will now solve the question in two ways, illustrating how to convert kilograms to pounds and then how to convert pounds to kilograms.

## Converting Kilograms to Pounds

Let’s convert John’s weight into pounds. If one kilogram is 2.2 pounds, then 66 kilograms is 66 x 2.2 = 145.2 pounds. Now, let’s divide it by 1.5, getting 96.8. The next step is easy: Jane needs to lose 110-96.8 = 13.2 pounds.

## Converting Pounds to Kilograms

Now, let’s solve the question in metric units:

John’s weight is 66 kg, so Jane wants to reach 66/1.5 = 44 kg. Her current weight is 110 pounds, which is 110 x 0.45 = 49.5 kg. This means that she needs to lose 49.5-44 = 5.5 kilograms. Converting back to pounds we get 5.5 x 2.2 = 12.1 pounds.

Okay, but wait a second…. Why is the answer different?

## The Drawbacks of Approximation

The answers differ because of approximation. Note that 2.2 x 0.45 is 0.99, which gives us 1 percent of error. Thus, we could get Jane's

weight in kilograms via 110/2.2. That would give us 50 kg, leading to 50-44 = 6, and 6 x 2.2 = 13.2. This was our answer in the first case. The difference of over 10% between the answers is a great illustration for the need for caution when using approximation in converting pounds to kilograms.

## An Exact Solution

If we want to solve the above question with extreme accuracy, we should use more decimal places in our calculations. Let’s do it quickly:

66 / 0.45359237 = 145.50509304

145.50509304 / 1.5 = 97.00339536

110 – 97.00339536 = 12.99660464

Now go and tell any “Jane” you know that she needs to lose 12.99660464 pounds and see the reaction… if you dare!

## References and Image Credits

WordIQ.com, at https://www.wordiq.com/definition/Pound

**Image Credits:**

https://js082.k12.sd.us/Notes_and_Wrkshts/Metric_Factor-Lable/metric_system_info.htm

https://www.matthewb.id.au/converter/grams-to-pounds-and-ounces-converter.html