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

Verified step by step guidance

1. Step 1: Understand the units of length given in the problem. These are all metric units used to measure length, but they differ by factors of ten.
2. Step 2: Recall the metric prefixes and their corresponding powers of ten: deci- means \$10^{-1}\(, milli- means \)10^{-3}\(, micro- means \)10^{-6}\(, and nano- means \)10^{-9}$ meters.
3. Step 3: Convert each unit to meters to compare their sizes directly: decimeter = \$10^{-1}\( m, millimeter = \)10^{-3}\( m, micrometer = \)10^{-6}\( m, nanometer = \)10^{-9}$ m.
4. Step 4: Compare the powers of ten for each unit. The smaller the exponent (more negative), the smaller the unit size.
5. Step 5: Identify the unit with the smallest power of ten (most negative exponent) as the smallest unit among the options.

Key Concepts

Metric Units of Length

Metric units measure length and are based on powers of ten. Common units include meters, decimeters (1/10 meter), millimeters (1/1000 meter), micrometers (1/1,000,000 meter), and nanometers (1/1,000,000,000 meter). Understanding their relative sizes helps compare small distances.

Order of Magnitude in Metric Units

Order of magnitude refers to the scale or size difference between units. For example, a nanometer is 1,000 times smaller than a micrometer, which is 1,000 times smaller than a millimeter. Recognizing these differences is essential to identify the smallest unit.

Application in Microbiology

Microbiology often deals with microscopic scales, where units like micrometers and nanometers describe sizes of cells, bacteria, and viruses. Knowing these units helps in understanding the scale of microorganisms and their components.