# Conversion factor

The conversion factor is a method used to convert a fraction. In this sense, from a fraction that expresses the relationship between two variables to another equivalent fraction, in which other units of measurement are used.

That is, the conversion factor method would allow us to convert, for example, kilometers per hour into meters per second, or go from pounds per square meter to kilograms per hectare.

This type of conversion is useful when we want or need to know the equivalences of certain indicators. For example, speed, weight or strength.

## Conversion factor method steps

To solve using the conversion factor method, we must know the relationship between the different units of measurement involved.

For example, suppose we need to give a patient medication based on their weight and the formula is in milliliters per kilogram. So if we know the weight of the person in pounds, the relationship between pounds and kilograms must also be known to calculate how many milliliters of the drug to consume.

The above will become clearer with the resolution of examples in the next section where what we do, in summary, is a multiplication of the equivalences.

## Conversion factor exercises

Next, let's look at some conversion factor exercises.

In the first example we develop the case that we had mentioned before.

Suppose that the indication to consume a drug is 1 milliliter per 10 kg and the person weighs 132,277 pounds. Also, we know that 1 kg equals 2.20462 pounds (lb).

Then:

1 ml / 10kg x 1kg / 2.20462lb = 0.04536 ml / lb

As we observed in the conversion, if we have kg in the numerator and in the denominator, it is as if this unit of measure was eliminated. Also, the fraction 1kg / 2.20462lb is equal to unity.

So the person should consume 0.04536 milliliters of the drug for every pound they weigh.

So if you weigh 132,277 pounds:

0.04536 × 132.277 = 6 milliliters approximately

Now, let's look at a more classic example with units of velocity.

If we have a car that can travel 120 kilometers per hour, how many meters can it travel per minute? We must remember that 1 kilometer is equal to 1,000 meters and that one hour is equal to 60 minutes.

Then:

120 km / h x 1,000m / km x 1h / 60min = 2,000 m / min

That is, the equivalent of 120 kilometers per hour is 2,000 meters per minute.

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