Problem 53 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. \(120 \mathrm{mg}=\)______ \(\mathrm{g}\)

Step-by-Step Solution

Answer

120 mg = 0.12 g.

Step 1: Understanding the Conversion

We need to convert milligrams (mg) to grams (g). The metric system uses base 10, so conversions involve moving the decimal point. 1 gram is equal to 1000 milligrams.

Step 2: Setting Up the Conversion

Since 1 gram equals 1000 milligrams, to convert milligrams to grams, we divide the number of milligrams by 1000.

Step 3: Performing the Division

Divide 120 mg by 1000 to get grams: \[\frac{120}{1000} = 0.12 \text{ g}\]

Step 4: Adjusting the Decimal

To divide by 1000, move the decimal point three places to the left. Starting with 120 (which is 120.0), move the decimal to the left three places to get 0.12.

Key Concepts

Decimal Movement

Understanding decimal movement is crucial when converting units in the metric system. This system is based on powers of 10, enabling us to easily convert between units by shifting the decimal point. When converting larger units to smaller units (e.g., grams to milligrams), you move the decimal point to the right, increasing the number. Conversely, converting from a smaller unit to a larger unit (like milligrams to grams) involves moving the decimal point to the left.
For example, if you start with a number like 120.0, moving the decimal three places to the left transforms it to 0.12. Each move to the left reduces the number by a factor of ten—a process fundamental in metric conversions.
Remember, the number of spaces you move corresponds to how many zeros are in the conversion factor, like 1000 in our milligrams to grams conversion.

Milligrams to Grams

Converting milligrams to grams is a common task when working with the metric system, particularly in contexts like science labs and medical dosages. Milligrams (mg) are a smaller unit of mass compared to grams (g). Specifically, 1 gram equals 1000 milligrams.
To better understand this relationship, consider the following points:

• 1 g = 1000 mg
• To convert milligrams to grams, you divide by 1000
• This conversion helps in simplifying measurements and calculations

Using this knowledge, converting milligrams to grams becomes straightforward. For example, if you have a dose of 120 mg, you know this translates into 0.12 g using the division by 1000 method.

Division by 1000

Performing division by 1000 is how we convert milligrams into grams. This process leverages the decimal system organization, facilitating easy calculations.
When you divide by 1000, you're practically moving the decimal point three places to the left. So, for the number 120 mg:

• If it's originally represented as 120.0, move the decimal three spots and it becomes 0.12 g
• This movement reflects the fact that 1000 milligrams make up a gram

It's handy to remember that every time you divide by a factor of 10,100, 1000, etc., you're simply shifting the decimal to the left by the corresponding number of zeros. This straightforward approach makes conversions in the metric system both fast and reliable.