# Converting 3.5 Grams to Ounces: Steps & Tutorial

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

What is the process for converting from grams to ounces? What are the hidden assumptions in this conversion? This lesson goes over both the process and the assumption associated with this type of conversion.

## Setting Up the Problem

Charlene has just completed a science lab where she measured the mass of a small object as being 3.5 grams. One of the questions in her assignment is to convert this mass measurement into a weight measurement with units of ounces. What are the steps to make this conversion? We'll take a closer look at the steps and assumptions necessary to make this conversion.

The first thing to realize about this conversion is that we are going from units of mass (grams) to units of weight (ounces). Although these concepts are closely related they are not the same thing. Mass is an intrinsic property of the material being considered, while weight is a combination of the mass of the object and the local acceleration of gravity.

The main difference between mass and weight is that mass does not change with location. The object Charlene measures in the science lab on earth would still have the same mass if it were somehow transported to the moon, deep space, or even the center of the Sun. The weight of the object in those same places would vary considerably.

This is all a long way of saying that there is an assumption built into converting mass units to weight units. That assumption is that the acceleration of gravity is fixed and will not change. This may seem like a pretty safe assumption, but once you know the acceleration of gravity on the surface of the earth can vary by almost a full percentage point, this turns out to be a larger assumption than you might have initially thought.

Once we've noted this assumption built into our conversion, we can use conversion factors to convert our units of mass to units of weight. Conversion factors are ratios of equivalent units used to convert from one set of units to another set of units. To get from one set of units to another just take the measurement in the units you have and multiply by the appropriate conversion factor.

In this case, however, we're going to have to multiply by two conversion factors. Why is that? Well, grams are the metric unit of mass, but the standard unit of weight is the pound, not ounces. Because of this, it is much more likely that you will be able to find a conversion factor for grams to pounds than for grams to ounces. To get to our final answer in ounces, we'll also have to multiply by the conversion factor for pounds to ounces. Our process is going to look like this:

(3.5 g) (conversion factor for grams to pounds) (conversion factor for pounds to ounces)

Now we should be able to look in a table of conversion factors or look it up online and find that 1 pound is equal to 453.6 grams. And 1 pound is also equal to 16 ounces. This makes our conversion factors:

(1 lb / 453.6 g) - conversion factor going from grams to pounds:

(16 oz / 1 lb) - conversion factor going from pounds to ounces:

To convert our mass of 3.5 g to ounces, we now substitute into our original expression to come up with the following:

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