Which of the following is smallest?
a. decimeter
d. millimeter
c. nanometer
d. micrometer

Verified step by step guidance

1. Identify the units of measurement given in the problem: decimeter, millimeter, nanometer, and micrometer.
2. Understand the metric system hierarchy: 1 meter (m) is the base unit, and the prefixes indicate fractions or multiples of a meter.
3. Convert each unit to meters: 1 decimeter (dm) = 0.1 meters, 1 millimeter (mm) = 0.001 meters, 1 micrometer (μm) = 0.000001 meters, 1 nanometer (nm) = 0.000000001 meters.
4. Compare the converted values to determine which is the smallest.
5. Conclude that the unit with the smallest value in meters is the smallest unit.

Key Concepts

Metric Units of Measurement

The metric system is a decimal-based system of measurement used globally, which includes units such as meters, centimeters, millimeters, micrometers, and nanometers. Each unit is a power of ten, making it easier to convert between them. Understanding these units is essential for comparing sizes accurately.

Order of Magnitude

Order of magnitude refers to the scale or size of a quantity in powers of ten. In the context of metric units, each step down (e.g., from millimeter to micrometer) represents a factor of ten smaller. This concept helps in quickly assessing the relative sizes of different units.

Nanometer

A nanometer (nm) is one billionth of a meter (10^-9 meters) and is commonly used to measure things at the atomic and molecular scale, such as wavelengths of light and sizes of molecules. It is significantly smaller than a micrometer (10^-6 meters), millimeter (10^-3 meters), and decimeter (10^-1 meters), making it the smallest unit in the provided options.