Question

6.put these units in order from smallest to largest:decimeter , meter ,kilometer,millimeter,centimeter,nanometer,micro meter.

Explanation:

Step1: Recall metric prefixes

Metric prefixes and their relationships:

• Nanometer (\( \text{nm} \)): \( 1\ \text{nm} = 10^{-9}\ \text{m} \)
• Micrometer (\( \mu\text{m} \)): \( 1\ \mu\text{m} = 10^{-6}\ \text{m} \)
• Millimeter (\( \text{mm} \)): \( 1\ \text{mm} = 10^{-3}\ \text{m} \)
• Centimeter (\( \text{cm} \)): \( 1\ \text{cm} = 10^{-2}\ \text{m} \)
• Decimeter (\( \text{dm} \)): \( 1\ \text{dm} = 10^{-1}\ \text{m} \)
• Meter (\( \text{m} \)): \( 1\ \text{m} = 10^{0}\ \text{m} \)
• Kilometer (\( \text{km} \)): \( 1\ \text{km} = 10^{3}\ \text{m} \)

Step2: Order by magnitude

Compare exponents of \( 10 \) (smaller exponent → smaller unit):

• Nanometer (\( 10^{-9}\ \text{m} \))
• Micrometer (\( 10^{-6}\ \text{m} \))
• Millimeter (\( 10^{-3}\ \text{m} \))
• Centimeter (\( 10^{-2}\ \text{m} \))
• Decimeter (\( 10^{-1}\ \text{m} \))
• Meter (\( 10^{0}\ \text{m} \))
• Kilometer (\( 10^{3}\ \text{m} \))

Answer:

nanometer, micrometer, millimeter, centimeter, decimeter, meter, kilometer