Question

Convert the following to the equivalent measures indicated. \(0.25 \mathrm{mg}=\) ______ \(\mathrm{mcg}\)

Short answer

0.25 mg is equal to 250 mcg.

Step-by-step solution

Understand the Relationship

To convert milligrams (mg) to micrograms (mcg), we need to understand that 1 milligram is equal to 1000 micrograms. This is because 'micro' means one millionth, and 'milli' means one thousandth, so 1 mg = 1000 mcg.

Set Up the Conversion

We have 0.25 mg, and we want to convert this to mcg. We will use the relationship 1 mg = 1000 mcg for the conversion. The setup will be a multiplication because we are converting to a smaller unit. Multiply the given amount in mg, which is 0.25, by 1000 mcg.

Perform the Calculation

Calculate the conversion by multiplying 0.25 mg by 1000 mcg/mg. This will convert the milligrams to micrograms.\[0.25 \times 1000 = 250\]

State the Result

The result of the calculation gives us the number of micrograms. \[0.25\, \text{mg} = 250\, \text{mcg}\]. So, 0.25 mg is equivalent to 250 micrograms.

Key concepts

Milligrams to Micrograms

When dealing with metric conversions, it's essential to understand how different units of measurement relate to each other. Here, we are focusing on converting milligrams (mg) to micrograms (mcg). A milligram is one-thousandth of a gram. On the other hand, a microgram is one-millionth of a gram. Therefore, in terms of micrograms, one milligram equals 1000 micrograms. Knowing this relationship is crucial because it forms the basis of converting between these two units. To put it simply, every time you see a 1 mg, you can immediately think of it as 1000 mcg. This understanding makes conversions straightforward and helps ensure accuracy in measurements, especially in fields like science and medicine where precision is key.

Unit Conversion Steps

Converting from one metric unit to another follows a systematic approach. Ensuring you follow these steps helps to avoid any mistakes. Let's go through the unit conversion steps used in our exercise:

• First, comprehend the relationship between the existing and target units. Here, we know 1 mg is equivalent to 1000 mcg.
• Next, set up your conversion. Since we are moving to a smaller unit (from mg to mcg), multiplication is the right operation. We multiply the quantity in milligrams by the conversion factor of 1000 mcg/mg.
• Finally, execute the calculation and arrive at the result.

Always break down the problem using these logical steps. This approach ensures clarity in more complex calculations, allowing for consistent results.

Mathematical Calculations

The actual mathematical calculations involved in metric conversions like milligrams to micrograms are straightforward once you understand the relationship between the units. Let's explain the calculation in our example:When given 0.25 mg to be converted into mcg, you'll use multiplication since you're converting to a smaller unit:\[ 0.25\, \text{mg} \times 1000\, \text{mcg/mg} = 250\, \text{mcg} \]Each of these terms is vital: - "0.25 mg" is your starting amount.- "1000 mcg/mg" is your conversion factor.By multiplying these values, you effectively increase the number of units to reflect their smaller size in the metric system. As a result, you find that 0.25 mg converts efficiently into 250 mcg. This method guarantees that measurements are precise, adhering to the initial conversion relationship between units. Remembering to perform these calculations with care is essential to maintaining accuracy in any task requiring unit conversions.