Problem 26 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. 950 mcg = ___________________________ mg

Step-by-Step Solution

Answer

950 mcg is 0.95 mg.

Step 1: Understand the Metric Prefixes

To convert micrograms to milligrams, we need to understand the metric prefixes. "Micro" (denoted as \(\mu\)) means one-millionth (\(10^{-6}\)) and "Milli" ("m") means one-thousandth (\(10^{-3}\)).

Step 2: Identify the Conversion Factor

For converting micrograms (mcg) to milligrams (mg), we calculate the difference in powers between milli and micro: \(10^{-3} - 10^{-6} = 10^{3}\). This means there are 1,000 micrograms in a milligram.

Step 3: Perform the Conversion

To convert 950 mcg to mg, use the factor from above: divide by 1,000 because there are 1,000 mcg in 1 mg. \[\frac{950 \text{ mcg}}{1,000} = 0.95 \text{ mg}\]

Step 4: Write the Final Answer

The final result of the conversion is 0.95 mg.

Key Concepts

Metric Prefixes

Metric prefixes are essential in understanding and converting measurements within the metric system. These prefixes indicate the scale or magnitude of a measurement. For example:

• "Micro" with the symbol \(\mu\), represents one-millionth, meaning \(10^{-6}\).
• "Milli" indicated by the letter "m," represents one-thousandth, which is \(10^{-3}\).

Knowing these prefixes helps us to express measurements accurately. This becomes particularly useful when converting measurements as it allows us to understand the relationship between the units, like micrograms (mcg) and milligrams (mg). By simply understanding the metric prefixes, you are one step closer to easily converting these measurements.

Conversion Factor

A conversion factor is a ratio used to convert one unit to another by multiplying or dividing a measurement by this factor. In the metric system, conversion factors often stem from the difference in the powers of ten between prefixes.

To successfully convert from micrograms to milligrams, determine the conversion factor by comparing the metric prefixes. Here's how it works:

• Micrograms are at \(10^{-6}\), and milligrams are at \(10^{-3}\).
• The conversion factor is derived from the difference in their exponents, which is \(10^{-3} - 10^{-6}\). Simplifying this gives you \(10^{3}\), or 1,000.

This tells us there are 1,000 micrograms in a milligram. Therefore, to convert micrograms to milligrams, you divide the number of micrograms by 1,000. Using a conversion factor is a straightforward way to ensure accurate conversions between units.

Decimal Movement

Decimal movement is key when converting within the metric system. This technique involves shifting the decimal point left or right, based on the conversion factor. It's a visual method that simplifies the arithmetic involved in metric conversion.

When converting from micrograms to milligrams, the conversion factor is 1,000. Hence:

• Since you're dividing by 1,000, you move the decimal point three places left. This is because 1,000 equals \(10^3\), indicating three decimal places.
• For instance, converting 950 micrograms (mcg) involves shifting the decimal three spots left, yielding 0.95 milligrams (mg).

Understanding decimal movement helps prevent mistake-prone calculations and offers a quick visual check of your metric conversions. This method effectively bridges knowing your prefixes and applying conversion factors for accurate results.