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

Verified step by step guidance

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.

Step 2: Recall the order of metric units from largest to smallest: decimeter (dm), millimeter (mm), micrometer (μm), and nanometer (nm).

Step 3: Convert each unit to meters to compare their sizes directly: 1 decimeter = 10\^{-1} meters, 1 millimeter = 10\^{-3} meters, 1 micrometer = 10\^{-6} meters, and 1 nanometer = 10\^{-9} meters.

Step 4: Compare the powers of ten in the conversions. The smaller the power of ten (more negative), the smaller the unit.

Step 5: Identify the unit with the smallest value in meters, which corresponds to the smallest unit among the options.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Metric Units of Length

Metric units measure length or distance and are based on powers of ten. Common units include meters, decimeters, millimeters, micrometers, and nanometers, each representing different scales from larger to smaller.

Order of Magnitude in Metric Units

Understanding the relative sizes of metric units involves knowing their prefixes: deci- (10^-1), milli- (10^-3), micro- (10^-6), and nano- (10^-9). Smaller prefixes indicate smaller units, so nanometers are much smaller than millimeters or decimeters.

Application of Metric Prefixes in Microbiology

In microbiology, measurements often require very small units like micrometers and nanometers to describe sizes of cells and molecules. Recognizing these units helps in accurately interpreting microscopic scales and comparing sizes.

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