Question

Convert the following metric measures by moving the decimal. \(276 \mathrm{~g}=\) ______ \(\mathrm{mg}\)

Short answer

276,000 mg

Step-by-step solution

Understand the Metric System

In the metric system, the prefix 'milli' means one-thousandth. Therefore, 1 gram (g) is equal to 1,000 milligrams (mg). We use this conversion factor to convert grams to milligrams.

Set Up the Conversion

Since 1 gram is equal to 1,000 milligrams, we need to multiply the number of grams by 1,000 to convert it to milligrams. We will multiply 276 grams by 1,000 to find the equivalent in milligrams.

Perform the Multiplication

Multiply 276 by 1,000:\[ 276 imes 1,000 = 276,000 \]Thus, 276 grams are equivalent to 276,000 milligrams.

Key concepts

Grams to Milligrams

Converting grams to milligrams is a common task in the metric system, especially in scientific and everyday applications. Grams and milligrams are both units of mass, with grams being the larger unit. Understanding how these two units relate is key to making conversions.

The prefix 'milli-' in milligram suggests the presence of "one-thousandth of a gram." Therefore, there are 1,000 milligrams in a single gram. This conversion factor (1 gram = 1,000 milligrams) makes it easy to switch between the units.

When you have a mass given in grams and need to convert it to milligrams, you multiply the number of grams by 1,000. For example, if you have 276 grams, you multiply by 1,000 to convert: \[ 276 ext{ g} imes 1,000 = 276,000 ext{ mg} \]This straightforward multiplication provides the mass in milligrams, making the conversion process simple and effective.

Decimal Movement in Metric Conversion

Decimal movement is an essential technique in the metric system, enabling easy conversion between units. The flexibility of the decimal system lies in its base-10 structure, which makes moving the decimal point straightforward.

When converting from a larger unit to a smaller unit, such as from grams to milligrams, you move the decimal point three places to the right. This shift reflects the multiplication by 1,000, which is the factor of conversion from grams to milligrams.

Consider converting 276 grams to milligrams: - Start with 276 (276.0). - Move the decimal point three places to the right. - This results in 276,000.0.

Thus, 276 grams equals 276,000 milligrams, without performing manual calculation. Understanding the idea of decimal movement helps streamline the conversion process and reduces errors.

Metric Prefixes

Metric prefixes are shorthand for powers of ten and serve as a foundational aspect of the metric system. Each prefix indicates a specific multiplier, simplifying large or small numbers.

Common prefixes include:

• Kilo- (k): Indicates 1,000 times the base unit (e.g., kilogram = 1,000 grams).
• Milli- (m): Represents one-thousandth of the base unit (e.g., milligram = 0.001 grams).
• Centi- (c): Means one-hundredth of the base unit (e.g., centimeter = 0.01 meters).

Using metric prefixes allows us to easily express measurements without resorting to scientific notation. This simplicity is thanks to our decimal-based system. Moving between these prefixes involves powers of ten, explained as shifts of the decimal point.

By mastering metric prefixes like milli- and understanding their role in conversion, navigating between units like grams and milligrams becomes intuitive.