Question

For each of the following pairs, which is the smaller unit? a. \(\mathrm{mg}\) or \(\mathrm{g}\) b. centimeter or millimeter c. \(\mathrm{mm}\) or \(\mu \mathrm{m}\) d. \(\mathrm{mL}\) or \(\mathrm{dL}\) e. \(\mathrm{mg}\) or \(\mathrm{Mg}\)

Short answer

a. \text{mg}, b. \text{millimeter}, c. \text{µm}, d. \text{mL}, e. \text{mg}

Step-by-step solution

- Compare milligrams and grams

A milligram (mg) is one-thousandth of a gram (g). Therefore, milligrams are smaller than grams.

- Compare centimeters and millimeters

A centimeter (cm) is equal to 10 millimeters (mm), so millimeters are smaller than centimeters.

- Compare millimeters and micrometers

A millimeter (mm) is equal to 1,000 micrometers (µm). Hence, micrometers are smaller than millimeters.

- Compare milliliters and deciliters

A milliliter (mL) is one-thousandth of a liter (L), while a deciliter (dL) is one-tenth of a liter. Thus, milliliters are smaller than deciliters.

- Compare milligrams and megagrams

A milligram (mg) is one-millionth of a megagram (Mg). Therefore, milligrams are much smaller than megagrams.

Key concepts

metric units

The metric system is a decimal-based system of measurement used around the world. It helps in making calculations simpler and converting between units straightforward. The most common metric units include meters for length, grams for mass, and liters for volume. Each of these units can be divided into smaller units or multiplied to create larger units using prefixes like milli- (one-thousandth), centi- (one-hundredth), and kilo- (one thousand). For instance, a meter can be broken down into millimeters, where 1 meter equals 1,000 millimeters.

measurement conversion

Measurement conversion is a crucial skill in understanding and comparing different units within the metric system. Knowing how to convert between units is important in various fields, from science to everyday life. For example, when comparing milligrams with grams, knowing that 1 gram equals 1,000 milligrams helps us see why a milligram is smaller. Here are some common conversions:

• 1 gram (g) = 1,000 milligrams (mg)
• 1 centimeter (cm) = 10 millimeters (mm)
• 1 millimeter (mm) = 1,000 micrometers (µm)
• 1 liter (L) = 1,000 milliliters (mL)
• 1 megagram (Mg) = 1,000,000 milligrams (mg)

These conversions allow us to easily switch between different unit sizes depending on the precision needed for a task.

comparison of units

Comparing units in the metric system involves understanding the relative sizes of the units in question. This is often made easier by their standard prefixes. Below are examples based on common comparisons:

• Milligram (mg) vs. Gram (g): A milligram is much smaller, as it is one-thousandth of a gram.
• Centimeter (cm) vs. Millimeter (mm): A millimeter is smaller since there are 10 millimeters in a centimeter.
• Millimeter (mm) vs. Micrometer (µm): Micrometers are smaller because 1 millimeter equals 1,000 micrometers.
• Milliliter (mL) vs. Deciliter (dL): A milliliter is smaller, with 1 deciliter equal to 100 milliliters.
• Milligram (mg) vs. Megagram (Mg): Milligrams are significantly smaller, with 1 megagram equaling 1,000,000 milligrams.

These comparisons demonstrate the varying scales of metric units, helping us to comprehend which units are more suitable for different measurements.