Question

Fill in the blank: \(1 \mathrm{mg}=\) _________ \(\mathrm{kg}\).

Short answer

1 mg = \(1 \times 10^{-6}\) kg.

Step-by-step solution

Understand the Units

The problem involves converting milligrams (mg) to kilograms (kg). We need to understand how these units relate to each other. 1 milligram is smaller than 1 kilogram.

Conversion Factors

The conversion factor between milligrams and kilograms is as follows: - 1 kilogram = 1,000,000 milligrams. This means that there are 1,000,000 milligrams in 1 kilogram.

Setting Up the Relation

To convert 1 mg to kg, use the conversion factor. Since there are 1,000,000 mg in 1 kg, each milligram is one-millionth of a kilogram.

Perform the Conversion

We calculate the conversion as follows: \[1 ext{ mg} = \frac{1}{1,000,000} ext{ kg}\] Thus, 1 mg equals \(1 imes 10^{-6}\) kg.

Key concepts

Milligram to Kilogram Conversion

When converting milligrams (mg) to kilograms (kg), it's essential to understand the size differences between these units of mass. Milligrams are much smaller than kilograms, and this scaling difference is a necessary aspect of metric system conversions.

Here's the basic idea:

• 1 kilogram (kg) is equivalent to 1,000,000 milligrams (mg).
• This conversion helps us understand that milligrams represent tiny amounts of a substance compared to kilograms.

To convert from mg to kg, we use the conversion factor to determine how many kilograms a given number of milligrams represents. For example with only 1 mg, it's necessary to understand that this small amount is just a fraction of a kilogram, specifically one-millionth.

The conversion is calculated using this factor by dividing the number of milligrams by 1,000,000. Thus, 1 mg equals \[1 \times 10^{-6} \text{ kg}\]. This shows a concise relationship between the two units, offering a clear path to complete conversions.

Conversion Factors in Chemistry

Conversion factors are an important tool in chemistry, facilitating the transformation of measurements from one unit to another. Essentially, they are simple ratios that express how many of one unit equals another unit. In the realm of chemistry, they are indispensable for analyzing chemical reactions and stoichiometry.

Conversion factors investigate and confirm the way in which different scales of measurement relate to one another. In our example of converting milligrams to kilograms, the conversion factor is:

• 1 kilogram = 1,000,000 milligrams.

Using this factor allows us to compute conversions accurately and ensures precise communication of chemical quantities thr negotiationg various scales. Remember, conversion factors allow measurements to be expressed in other terms without changing the inherent value; they simply provide clarity across diverse units.

Steps in Unit Conversion

Converting units in chemistry or any other field is often a systematic process, composed of a few clear steps. Let’s break it down to make it easier to follow:

• Identify the Units: Start by clearly identifying the units involved in the conversion. In our example, these are milligrams and kilograms.
• Determine the Conversion Factor: Use known data to write down the conversion factor. For milligrams and kilograms, it's essential to remember that 1 kg equals 1,000,000 mg.
• Set up the Conversion Equation: Arrange your equation to utilize the conversion factor, ensuring it cancels out the initial unit and introduces the new one.
• Perform the Calculation: Conduct the arithmetic operation. In this case, take the number of milligrams and divide by 1,000,000 to get the equivalent number in kilograms.
• Double-Check Your Work: Ensure that the conversion makes logical sense and that units are canceled and introduced correctly.

These steps, executed systematically, can be applied to almost any unit conversion question, allowing clear and accurate solutions.