Question

Convert the following metric measures by moving the decimal. \(36.5 \mathrm{mg}=\) ______ \(\mathrm{g}\)

Short answer

36.5 mg is 0.0365 g.

Step-by-step solution

Understanding the Conversion Factor

To convert from milligrams (mg) to grams (g), we need to understand that 1 gram is equal to 1000 milligrams. This means to convert milligrams to grams, we divide the number of milligrams by 1000.

Performing the Division

Given that we have 36.5 milligrams, we apply the conversion factor. We divide 36.5 by 1000 to convert it to grams.\[ 36.5 \, \text{mg} \times \frac{1 \, \text{g}}{1000 \, \text{mg}} = 0.0365 \, \text{g} \]

Moving the Decimal

Since dividing by 1000 is equivalent to moving the decimal point three places to the left, we can also achieve this by taking 36.5 and shifting the decimal three positions to the left. This confirms the conversion: 36.5 mg becomes 0.0365 g.

Key concepts

Milligrams to Grams

In the world of metric conversions, understanding the relationship between units is crucial. Milligrams (mg) and grams (g) are both units of weight used to measure mass in the metric system. However, they represent different scales. It is important to note that 1 gram is equivalent to 1000 milligrams. This means that a gram is a much larger unit compared to a milligram. For practical purposes, when converting milligrams to grams, we use the conversion factor that 1 gram is equal to 1000 milligrams. This straightforward relationship allows us to easily convert from milligrams to grams by utilizing simple division. Remembering the conversion factor is key to mastering metric conversions.

Decimal Movement

Decimal movement is an easy method for converting between different metric units. When you hear the term "decimal movement," it's simply referring to the shifting of the decimal point in a number for conversion purposes.

In our example, to convert milligrams to grams, think of moving the decimal point three spaces to the left. This is because there are three zeros in the number 1000, reflecting the scale difference between milligrams and grams.

For instance, starting with 36.5 mg, you can move the decimal point from its original location to three places left, turning the number into 0.0365 g. This method is a handy mental shortcut that lets you convert quickly without complex calculations. Always be careful with the decimal movement to ensure accuracy.

Division in Conversions

Division in conversions is one of the foundational principles in metric system calculations. When converting units like milligrams to grams, the process involves dividing by the conversion factor.

For milligrams to grams, the conversion factor is 1000. Hence, you divide the milligram value by 1000. Why division? Because you are converting to a larger unit, which means you have fewer grams compared to milligrams.

In our example with 36.5 mg, you divide 36.5 by 1000. Doing this calculation, \[ 36.5 \times \frac{1}{1000} = 0.0365 \] shows you have 0.0365 grams.

This method ensures precision in your conversion, and understanding it solidifies your grasp on metric conversions.