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Kilograms to Pounds

Here's a prehistoric example to get things started.

We find out that $22,500\text{ kilograms (kg)}$ is equal to the mass of a T-rex, on average. You like to measure weight using pounds (lbs). You decide to ask your math teacher how many pounds the T-rex weighs, but she gives you the unit rate for kg to lbs.

$$1\text{ kilogram}\approx 2.2\text{ pounds}$$

She expects you to convert kg to lbs yourself. Typical.

The conversion rate

$$1\text{ kilogram}\approx 2.2\text{ pounds}$$

means $1\text{ kilogram}$ and $2.2\text{ pounds}$ are defined as being equal.

Example: Converting Kg to Lb

Let's set up a conversion table to help us. We know the T-rex weighs $22{,}500\text{ kg}$. $$\begin{array}{c|c|c} 22{,}500\text{ kg}\\ \hline \end{array}$$ We also know that $2.2\text{ lbs}$ is approximately $1\text{ kg}$. $$\begin{array}{c|c|c} 22{,}500\text{ kg}&2.2\text{ lbs}\\ \hline &1\text{ kg} \end{array}$$ Since kilograms are above and below the fraction bar, we can cancel them out. $$\begin{array}{c|c|c} 22{,}500\cancel{\text{ kg}}&2.2\text{ lbs}\\ \hline &1\cancel{\text{ kg}} \end{array}$$ This tells us that a T-rex weighs $22{,}500\cdot2.2\text{ lbs}$. $$22{,}500\cdot2.2=\boxed{49{,}500\text{ lbs}}$$

The example above walked you through using conversion tables to change kg to lbs. Now try reversing the conversion in the example below.

Practice: Converting Lb to Kg

$$\begin{align} 500 \text{ pounds} \cdot \frac{1 \text{ kilogram}}{ 2.2 \text{ pounds}} &= 500 \,\cancel{\text{ pounds}} \cdot \frac{1 \text{ kilogram}}{ 2.2 \cancel{\text{ pounds}}} \\ &= \frac{500}{2.2} \text{ kilograms} \\ &\approx \boxed{227 \text{ kilograms}} \\ \end{align}$$

(Video) Converting Pounds to Kilograms

by T Wood

The above video by T Wood shows how to convert from pounds to kilograms. Throughout we abbreviate kilograms with the symbol kg. We also abbreviate pounds with the symbol lb.

$\large{\text{Summary}}$

We need to keep in mind the unit rate to convert from kilograms to pounds (kg to lbs): $$\boxed{1\text{ kg}=2.205\text{ lbs}}$$

Suppose you wanted to convert $25$ lbs to kg. We can do this by setting up a conversion table. For this problem, divide by the decimal $2.205$ and cancel out the pound units: $$\begin{array}{c|c} 25\text{ lbs}&1\text{ kg}\\ \hline &2.205\text{ lbs} \end{array}$$ $$\begin{array}{c|c} 25\cancel{\text{ lbs}}&1\text{ kg}\\ \hline &2.205\cancel{\text{ lbs}} \end{array}\approx \boxed{11.38}\text{ kg}$$

Your friend, who's on vacation in the United Kingdom at the moment, emails you about a large fish he caught. He tells you that when he weighed it using the scale in their house, it was $22.4 \text{ kilograms} (kg)$! However, he has no idea exactly how heavy it is, since he's not from the United States and isn't used to measuring things in pounds (lbs). Perhaps this is because kilograms are the base unit of mass! How do you figure out how much the fish weighs in pounds? We convert kg to pounds. But how? Let's find out.

To find the fish's weight (or mass) in pounds, we convert its weight from kilograms to pounds by using the unit rate $$\text{lb}=2.2 \cdot \text{kg}$$ where $\text{lb}$ is the number of pounds and $\text{km}$ is the number of kilograms.

This gives us an approximate measure of how much the fish weighs, which is around $2.2\cdot22.4=\boxed{49.28}$ pounds. That's one heavy fish!

Now let's say your friend told you it weighed $22.4$ pounds instead, and he wanted to tell another friend, who lives in England, how much it weighed in kilograms. We can apply a similar formula to convert pounds to kilograms. $$\text{kg}=0.45 \cdot \text{lb}$$ where $\text{lb}$ is the number of pounds and $\text{kg}$ is the number of kilograms.

In kilograms, the fish weighs around $0.45\cdot22.4=\boxed{10.08} \text{ kilograms}$. If you're interested, you can also convert between kilograms and grams.