Question

Convert the following to the equivalent measures indicated. \(36 \mathrm{mg}=\) ______ \(\mathrm{g}\)

Short answer

36 mg is equal to 0.036 g.

Step-by-step solution

Identify the Conversion Factor

To convert milligrams (mg) to grams (g), we use the conversion factor that 1 gram is equal to 1000 milligrams. This allows us to switch between the two units.

Set up the Conversion Equation

Using the conversion factor, we set up the equation: \[ 36 \text{ mg} \times \left( \frac{1 \text{ g}}{1000 \text{ mg}} \right) \]This equation will allow us to convert milligrams to grams.

Perform the Calculation

Multiply the given quantity by the conversion factor:\[ 36 \times \frac{1}{1000} = 0.036 \]So, 36 mg is equivalent to 0.036 g.

Key concepts

Measurement

Understanding measurement is crucial when working with unit conversions. Measurement isn't just about numbers; it involves comparison to a standard unit. Whether you're measuring weight, length, or volume, you need a starting reference point. Here, our focus is on weight and converting a smaller weight unit, milligrams, to a larger one, grams.
Different countries and scientific fields may prefer different measurement systems. It's vital to be aware of the units you're dealing with, especially when converting between them. This awareness makes your calculations accurate.
When converting between units, always mark down the unit you're working with to avoid confusion. This way, you ensure the integrity of your operations and conclusions.

Conversion Factor

The conversion factor plays a vital role in converting one measurement unit to another. Essentially, it's a number that you multiply your initial measurement by, to switch between units. Think of a conversion factor as a bridge that connects two different units. Each side of the bridge represents a unit, and it enables you to traverse from one side, or unit, to the other.
For instance, in the conversion from milligrams to grams, the conversion factor is 1 gram per 1000 milligrams. This means that for every 1000 milligrams, you have one gram. It helps you understand the proportion or relationship between the two units and confidently perform the calculations needed.

Milligrams to Grams

Milligrams and grams are both metric units of mass, but they vary vastly in size. Converting milligrams to grams involves understanding these differences.
A milligram is one-thousandth of a gram:

• 1 gram = 1000 milligrams
• Therefore, 1 milligram = 0.001 grams

This means you have to divide the number of milligrams by 1000 to get the equivalent in grams. Knowing this conversion is helpful when handling small masses, such as medicines or small snacks, which are often measured in milligrams.

Mathematics

Mathematics is involved in almost every aspect of unit conversions. While performing a conversion from milligrams to grams, you rely on a simple mathematical operation, multiplying fractions, to change units.
The mathematics of conversion factors involves creating a fraction where one unit is compared to another. For example, when converting 36 milligrams to grams, you use the conversion factor of \(\frac{1 \text{ gram}}{1000 \text{ milligrams}}\). Multiply this by the given quantity (36 mg) to find the equivalent value in grams:
\[36 \text{ mg} \times \frac{1 \text{ gram}}{1000 \text{ mg}} = \frac{36}{1000} \text{ grams} = 0.036 \text{ grams}\]
It's important to master these mathematical principles to perform unit conversions accurately and with confidence.