Question

Convert the following to the equivalent measures indicated. \(1.8 \mathrm{mg}=\) ______ \(\mathrm{g}\)

Short answer

1.8 mg = 0.0018 g

Step-by-step solution

Understand the Units

The problem asks us to convert milligrams (\(\mathrm{mg}\)) to grams (\(\mathrm{g}\)). It is important to recognize the relationship between these two units. There are 1000 milligrams in 1 gram.

Setup the Conversion Factor

Using the relationship between milligrams and grams, we know that \(1 \mathrm{mg} = \frac{1}{1000} \mathrm{g}\). This conversion factor will help us change milligrams to grams.

Calculate the Conversion

To convert \(1.8 \mathrm{mg}\) to grams, multiply \(1.8\) by the conversion factor \(\frac{1}{1000}\):\[1.8 \mathrm{mg} \times \frac{1}{1000} = 0.0018 \mathrm{g}.\]

State the Result

After the conversion, \(1.8 \mathrm{mg}\) is equal to \(0.0018 \mathrm{g}\).

Key concepts

Metric System

The Metric System is a decimal-based system of measurement used worldwide. It's designed to make conversions between units easy by utilizing powers of ten. This system includes meters for lengths, kilograms for mass, and liters for volume, among others. The Metric System is especially favored in scientific and mathematical applications because of its simplicity and precision.

When working within this system, each unit is associated with a power of ten. This is consistent across various measurements:

• Kilo- means a factor of 1000 (e.g., 1 kilometer = 1000 meters).
• Centi- means a factor of 1/100 (e.g., 1 centimeter = 0.01 meters).
• Milli- means a factor of 1/1000 (e.g., 1 millimeter = 0.001 meters).

By having this systematic approach, transitioning between these units becomes intuitive, as demonstrated by converting milligrams to grams.

Milligrams to Grams

Converting Milligrams to Grams is a straightforward process in the Metric System. Understanding the relationship between these units is critical:

• Milligram (mg) is a unit of mass equal to one-thousandth (1/1000) of a gram (g).
• Therefore, 1 milligram equals 0.001 grams.

To perform the conversion, you use this relationship as a conversion factor. For example, when you convert 1.8 mg to grams:- Multiply by the conversion factor: \[1.8 \, \text{mg} \times \frac{1}{1000} = 0.0018 \, \text{g}\]This simple multiplication illustrates how milligrams are a smaller measurement than grams, requiring several milligrams to equal just one gram.

Mathematical Calculation

Mathematical Calculation is key when converting measurements. It involves understanding and applying conversion factors accurately. In our example of converting 1.8 mg to grams, the following steps are involved:

• Identify the conversion factor between the units.
• Multiply the amount in milligrams by the conversion factor.

The conversion factor for milligrams to grams is \(\frac{1}{1000}\), meaning each milligram equals 0.001 grams. Thus, for 1.8 mg:

• Calculation: \[1.8 \, \text{mg} \times \frac{1}{1000} = 0.0018 \, \text{g}\]

Always ensure your calculations are accurate, e.g., by checking units and using a consistent method for all conversions.

Measurement Units

Measurement Units are critical in understanding and expressing quantities. They allow us to convey precise information about the size, length, mass, and volume of objects.

In the Metric System, units are standardized, making them universally accepted and understood:

• Length is measured in meters (m), centimeters (cm), millimeters (mm), etc.
• Mass is measured in grams (g), kilograms (kg), milligrams (mg), etc.
• Volume is measured in liters (L), milliliters (mL), cubic centimeters (cc), etc.

By using consistent units, we ensure universal understanding and communication, removing ambiguities in scientific and everyday contexts. Acknowledging the relationship between units, such as converting milligrams to grams, showcases the practical utility of understanding measurement units.