# Converting 1 Gram to Milliliters: How-to & Steps

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Converting between grams and milliliters might be a little more complicated than you expect. We'll see how to make this conversion by converting one gram of powdered sugar to milliliters.

## Steps to Solving the Problem

Imagine you find yourself working a simple chemistry experiment that has you mixing a solution of powdered sugar and water. The experiment asks for one gram of sugar to be mixed with the water, but the only thing you have to measure the sugar is a beaker marked in milliliters. You remember that one gram of water equals one milliliter of water. So shouldn't one gram of sugar equal one milliliter of sugar? Well, it turns out to be a little more complicated than that.

Unlike a conversion, such as inches to centimeters, where one inch will always equal 2.54 centimeters, one gram can equal varying amounts of milliliters depending on what substance you're measuring. This is because grams and milliliters are units for different types of measurements, which is unlike inches and centimeters which both measure length. A gram is a unit of mass, and a milliliter is a unit of volume. To convert between the two, we need a third property of the material that relates them, and it turns out that property is density.

Density (D) equals mass (m) divided by volume (V). You need to know the density of what you're trying to convert from grams to milliliters. Let's say our powdered sugar has a density of 0.80 g/ml. This is our conversion factor, and we can use this to convert any amount of powdered sugar from grams to milliliters.

To convert one gram of powdered sugar to milliliters we start with the equation for density.

D = m / V

We are trying to find milliliters, which is volume in this equation. So we need to get volume by itself on one side of the equation. To do this we start by multiplying both sides of the equation by volume.

D * V = (m * V) / V

We know that any number divided by itself equals one.

D * V = m * 1

We also know that any number multiplied by one equals itself.

D * V = m

The shorthand commonly used for the two steps above is saying that the volumes on the right of the equation sign cancel each other out.

Next, we divide both sides of the equation by density in order to cancel it out on the left of the equation sign.

(D * V) / D = m / D

V = m / D

Now that we have volume by itself, we put in 1 g for our mass and 0.80 g/ml for our density.

V = 1 g / 0.80 g/ml

V = 1.3 ml

## Solution

There is no single solution for converting one gram to milliliters. What you get will depend on the density of the substance you are converting from grams to milliliters. In our example we found that 1 g of powdered sugar with a density of 0.80 g/ml equals 1.3 ml.

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