For each of the following pairs, which is the larger unit?
a. milligram or kilogram

Verified step by step guidance

1. Understand the metric prefixes: 'milli-' means 1/1000 (10⁻³) and 'kilo-' means 1000 (10³). These prefixes indicate the scale of the base unit, which in this case is the gram (g).
2. Compare the two units: A milligram (mg) is 1/1000 of a gram, while a kilogram (kg) is 1000 grams. This means that 1 kilogram is much larger than 1 milligram.
3. Express the relationship mathematically: 1 kilogram (kg) = 10³ grams (g), and 1 milligram (mg) = 10⁻³ grams (g). Therefore, 1 kilogram = 10⁶ milligrams.
4. Conclude that since 1 kilogram is equivalent to 1,000,000 milligrams, the kilogram is the larger unit in this pair.
5. Remember that understanding metric prefixes and their powers of ten is key to comparing units in the metric system.

Key Concepts

Metric System

The metric system is a decimal-based system of measurement used globally, which includes units such as meters for length, liters for volume, and grams for mass. It is structured around powers of ten, making conversions between units straightforward. Understanding the metric system is essential for comparing different units of measurement, such as milligrams and kilograms.

Units of Mass

Units of mass are standard measures used to quantify the amount of matter in an object. In the metric system, common units include milligrams (mg), grams (g), and kilograms (kg). Knowing the relationship between these units is crucial for determining which is larger; for instance, 1 kilogram equals 1,000,000 milligrams.

Conversion Factors

Conversion factors are numerical values used to convert one unit of measurement to another. In the context of mass, they allow for the comparison of different units, such as converting milligrams to kilograms. Understanding how to apply conversion factors is key to answering questions about which unit is larger.