Question

Convert the following to the equivalent measures indicated. \(1 \mathrm{mg}=\)______ g

Short answer

1 mg = 0.001 g.

Step-by-step solution

Identify the Conversion Factor

The conversion factor between milligrams and grams is that 1 gram equals 1000 milligrams. This means that you can use the conversion factor of 1 mg = 0.001 g to convert milligrams to grams.

Convert Milligrams to Grams

Use the conversion factor to convert 1 mg into grams. The equation is:\[1 \, \text{mg} \times 0.001 \, \text{g/mg} = 0.001 \, \text{g}\]So, 1 mg is equal to 0.001 g.

Key concepts

Understanding Conversion Factors

A conversion factor is a value used to change the units of a quantity without changing its value. Essentially, it acts as a bridge enabling you to convert one unit type to another, like milligrams to grams.
Understanding conversion factors is crucial for solving many math problems involving different units. They are often presented in the form of a fraction or ratio that equals one.
For example, to convert milligrams (mg) to grams (g), you use the conversion factor \(1 \, \text{g} = 1000 \, \text{mg}\). This means 1 gram equals 1000 milligrams.
When using a conversion factor, always multiply by the factor that cancels out the unit you want to change from. Here, multiply by \(0.001 \, \text{g/mg}\) to convert from mg to g.

From Milligrams to Grams: How it Works

Converting from milligrams to grams is a common unit conversion in both science and everyday life.
Milligrams and grams are both units of mass in the metric system, which is designed for easy conversion. Since there are 1000 milligrams in a gram, the conversion process involves division.
To convert milligrams to grams, use this simple formula: divide by 1000, which is the result of the conversion factor \(1 \, \text{mg} = 0.001 \, \text{g}\). An easier way to think of it might be: move the decimal point three places to the left in the milligram value.
So if you have 1 mg, once you apply the conversion factor, \(1 \, \text{mg} \times 0.001 \, \text{g/mg} = 0.001 \, \text{g}\), you get the result in grams.

Basic Math Operations in Unit Conversion

Basic math operations like multiplication and division are fundamental to unit conversion tasks.
For converting milligrams to grams, multiplication is key when you apply the conversion factor.

• First, state what you know: the conversion factor (1 mg = 0.001 g).
• Then, set up the equation using this factor: for instance, \(1 \, \text{mg} \times 0.001 \, \text{g/mg} = 0.001 \, \text{g}\).
• The final step is multiplying across to complete the conversion.

These simple operations ensure you convert units correctly, and are essential for precision in scientific calculations. Consistency in using these math operations fosters confidence in students as they encounter more complex unit conversions in their studies.