Question

Convert the following metric measures by moving the decimal. \(150 \mathrm{~g}=\) ______ \(\mathrm{mg}\)

Short answer

150,000 mg

Step-by-step solution

Understand the Relationship

To convert grams to milligrams, understand that 1 gram is equivalent to 1000 milligrams. This is because the prefix 'milli-' means a thousandth, hence 1000 milligrams make up 1 gram.

Set Up the Conversion

Begin with the given value in grams, which is \(150\) grams. We want to convert this to milligrams.

Perform the Conversion

Since 1 gram = 1000 milligrams, multiply \(150\) grams by \(1000\). This gives: \(150 \times 1000 = 150000\) milligrams.

Adjust the Decimal Position

By multiplying by \(1000\), you effectively move the decimal point three places to the right. So, \(150.0\) becomes \(150000.0\), which is \(150000\) when expressed as milligrams.

Key concepts

Decimal Movement

Decimal movement is a fundamental concept in metric conversion, which involves shifting the decimal point in a number based on the units you're converting between. When converting larger units to smaller ones, you move the decimal to the right. Conversely, when converting smaller units to larger ones, you move the decimal to the left.
For example, when converting from grams to milligrams, since 1 gram is equal to 1000 milligrams, you move the decimal point three places to the right. This is because multiplying by 1000 involves three factors of 10 (i.e., 10 x 10 x 10 = 1000).
Visualizing decimal movement can help you better understand the conversion process:

• Starting with 150 grams, represented as 150.0, you move the decimal three spots to the right.
• Each move represents multiplying by 10, eventually converting 150.0 grams to 150,000.0 milligrams.

This method saves time and reduces errors when dealing with metric conversions, as it avoids lengthy calculations.

Grams to Milligrams

Converting grams to milligrams is a common metric conversion. This involves understanding the meaning behind metric prefixes. Grams (g) are a base unit of mass in the metric system, while milligrams (mg) are a smaller unit derived from grams.
The prefix 'milli-' means one-thousandth, hence it requires 1000 milligrams to make up 1 gram. Recognizing this relationship is key to converting between these units.
When you have a mass measured in grams and need it in milligrams, remember to multiply your gram value by 1000:

• Given: 150 grams
• Multiply by 1000 to convert: 150 x 1000 = 150,000 milligrams

This straightforward multiplication leverages the metric system's use of base ten, making it easier to move between unit sizes.

Measurement Conversion

Measurement conversion is a technique used to change a given measurement from one unit to another within a system like the metric system. It is critical for ensuring that measurements are in the appropriate unit for context, accuracy, and clarity.
The metric system simplifies conversion through uniform use of prefixes like 'milli-', 'centi-', and 'kilo-', which denote scaling factors based on powers of ten. This uniformity allows for easy conversion using multiplication or division.

• Converting within the metric system usually requires knowing the conversion factor between units.
• For example, converting grams to milligrams involves a conversion factor of 1000.

To execute a measurement conversion:

• Identify the relationship between the starting and ending units.
• Apply the conversion factor: In the grams to milligrams example, multiply the number of grams by 1000 to find the equivalent milligrams.

Understanding these factors ensures precise measurements and enhances problem-solving skills.

Mathematical Operations

Mathematical operations, such as multiplication and division, play an essential role in converting measurements. These operations allow for effective manipulation of numbers to switch between different units without changing the inherent value of the measurement.
In the context of converting grams to milligrams, you primarily use multiplication. This operation scales the measurement up because milligrams are a smaller unit than grams, thus requiring more milligrams to represent the same mass.

• Step 1: Identify the initial measurement, e.g., 150 grams.
• Step 2: Use multiplication with the conversion factor, which in this context is 1000: 150 multiplied by 1000 equals 150,000.
• Alternatively, to convert in the opposite direction, division would be employed.

These operations depend on understanding and applying the appropriate conversion factor, which stems from the metric unit relationship. Mastery of these principles will aid in various mathematical tasks involving unit conversions.