Question

Convert the following metric measures by moving the decimal. \(250 \mathrm{mcg}=\) ______ \(\mathrm{mg}\)

Short answer

250 mcg is 0.25 mg.

Step-by-step solution

Understand the Metric Conversion

To solve this problem, we need to convert micrograms (mcg) to milligrams (mg). Recall that 1 mg equals 1,000 mcg. Therefore, to convert mcg to mg, we divide the number of mcg by 1,000.

Set Up the Equation for Conversion

Given 250 mcg, the conversion equation is: \[ \text{mg} = \frac{250 \text{ mcg}}{1000} \]

Perform the Division

Divide 250 by 1,000 to convert mcg to mg. \[ 250 \div 1000 = 0.250 \]

Write the Final Answer

Therefore, 250 mcg is equal to 0.250 mg. You can also write it simply as 0.25 mg, since trailing zeros after the decimal in non-scientific numbers don't affect value.

Key concepts

Micrograms to Milligrams

When converting micrograms (often abbreviated as mcg) to milligrams (mg), it's crucial to remember the basic relationship between the two units. - **Micrograms and milligrams**: In the metric system, these measurements indicate mass and weight. - **Conversion relationship**: 1 milligram is equal to 1,000 micrograms. This means that if you have a certain amount of micrograms, you need to divide by 1,000 to convert it to milligrams. For example, if you have 250 micrograms and want to convert it to milligrams, divide 250 by 1,000. The calculation looks like this: \[ \frac{250 \text{ mcg}}{1000} = 0.25 \text{ mg} \] This straightforward process helps ensure that you can easily move between different units of measurement using simple division. Each time you need to convert micrograms to milligrams, remember to divide by 1,000, as there are 1,000 mcg in 1 mg.

Decimal Movement in Conversions

Understanding decimal movement can be one of the simplest ways to manage conversions in the metric system. When you divide by 1,000, you essentially move the decimal point three places to the left. - **Aligning the decimal**: In the example of converting 250 mcg to mg, think of 250 as 250.0. - **Shifting the decimal**: Moving the decimal three places left turns 250.0 into 0.250. Each movement reflects a division by 10, so moving it three places left divides by 1,000. Therefore, 250.0 becomes 0.250, or simply 0.25, since the trailing zero does not change the value in decimal numbers. This method offers a visual way to conceptualize the conversion process without always relying on a calculator. It's particularly useful in settings where quick mental conversions are needed.

Metric System

The metric system is a globally adopted decimal-based system of measurement. Understanding this system is critical in science, medicine, and everyday life. - **Base units**: The metric system uses base units like meters for length, liters for volume, and grams for mass. - **Consistency and ease**: Since it's a decimal system, conversions are consistent and simple. Small units like micrograms can be easily converted to larger ones like milligrams or grams by moving the decimal. For example, 1 milligram (mg) is in turn 0.001 grams (g). Each step involves multiplying or dividing by powers of ten, reflecting the system's logic and ease of use. After mastering the basics of metric conversions, you can adeptly handle metric-related exercises. This makes tasks like converting micrograms to milligrams straightforward, supporting both learning and practical applications in real-world scenarios.