Gramas<-->quilogramas

A kilogram is $1{,}000$ grams

For every kilogram, there are $1000$ grams. That means that the ratio between kilograms and grams is $1:1000$. It also means $1$ kilogram and $1000$ grams are defined as being equal.

Traditionally, grams are referred to as the base unit. That means we usually start in grams, and convert to kilograms. However, it's important to know how to convert both ways. Also, you may want to convert between systems of measurement. There is a conversion between kilograms and pounds.

For now though we'll focus on converting between kilograms and grams.

When we want to convert from kilograms to grams, we can just multiply by: $$\frac{1{,}000\text{ grams (g)}}{1\text{ kilograms (kg)}}$$

When we want to convert from grams to kilograms, we can do the reverse: multiply by: $$\frac{1\text{ kg}}{1{,}000\text{ g}}$$

So, if we want to convert $1$ kg to g, we can do the following:

$$1\text{kg} \times \frac{1000\text{ g}}{1\text{ kg}} = \frac{1\text{ kg} \times 1000\text{ g}}{1\text{ kg}} = 1000\text{ g}$$

We could also convert from grams to kilograms, then back to grams. In this case, we should get the answer we started with. It serves as a way to check your work, and it gives you extra practice!

$$123\text{ g} \times \frac{1\text{ kg}}{1000\text{ g}} = 123\cancel{\text{ g}} \times \frac{1\text{ kg}}{1000\cancel{\text{ g}}} = \frac{123\text{ kg}}{1000} = \boxed{0.123\text{ kg}}$$

So, $123$ grams is equal to $0.123$ kilograms.

There are $1{,}000$ grams in one kilogram. Kilo means $1{,}000$—think kilometers and meters. This is part of an example of a system of units, the metric system.

Multiply to convert bigger to smaller units, divide to convert smaller to bigger units!

Using multiplication to convert kilograms to grams. Divide, on the other hand, to convert grams to kilograms. And cancel out the units you don't need along the way.

For example, if you're converting from kilograms to grams, the kilograms should cancel out. Your final answer should ONLY have grams. The reverse is also true. If you convert from grams to kilograms, the grams should cancel out.

Try it!

$$\begin{align} 382 \text{ grams} \cdot \frac{1 \text{ kilogram}}{1000 \text{ grams}} &= 382 \cancel{\text{ grams}} \cdot \frac{1 \text{ kilogram}}{1000 \cancel{\text{ grams}}} \\ &= \frac{382}{1000} \text{ kilograms} \\ &= \boxed{0.382 \text{ kilograms}} \\ \end{align}$$

(Video) Convert Kilograms to Grams

by larryschmidt

This video by larryschmidt goes through a more complicated conversion of units.

$\large{\text{Summary}}$

Normally, we've been seeing problems where we had to convert one unit. But what if there are multiple conversions to be done? A simple way to do this is using a conversion table. Let's look at an example and work through it to see how it's done.

Suppose you want to convert $3 \text{ kg/L}$ to $\text{g/mL}$. These are unit rates, because the units are a ratio of two other units. Each of these unit rates are an amount of mass per unit of volume.

Start by writing down the known information. $$\begin{array}{c|c} 3\text{ kg}&\\ \hline \text{L}& \end{array}$$

The first conversion we want to make is turning kilograms into grams. Actually we can do the steps in multiple orders, but we'll show you how it works this way.

In the next two boxes, write down this conversion. Make sure $\text{kg}$ is in the bottom box so that it can cancel out with the one above.

$$\begin{array}{c|c} 3\text{ kg}&1000\text{ g}&\\ \hline \text{L}&1\text{ kg}& \end{array}$$

We'll do all the cancellations at the end. Next, we want to convert from $\text{L}$ to $\text{mL}$. We write this conversion in the next two boxes. Make sure that $\text{L}$ is in the top box so that it can cancel with the one in the bottom.

$$\begin{array}{c|c} 3\text{ kg}&1000\text{ g}&1\text{ L}\\ \hline \text{L}&1\text{ kg}&1000\text{ mL} \end{array}$$

We can cancel units. $$\begin{array}{c|c} 3\cancel{\text{ kg}}&1000\text{ g}&1\cancel{\text{ L}}\\ \hline \cancel{\text{L}}&1\cancel{\text{ kg}}&1000\text{ mL} \end{array}$$

Finally, write our answer as a single fraction. $$\frac{3\times1000\times1}{1\times1000}=3\frac{\text{g}}{\text{mL}}$$