High School

List and arrange the following units in order from largest to smallest:

\[ m^3, \, mL, \, cL, \, \mu L, \, L, \, dL. \]

Answer :

To arrange the given units from largest to smallest, we need to understand their equivalence in terms of a common unit. We will use liters (L) as our common unit for comparison. Here are the conversion factors for each unit to liters:

1. Cubic meter (m^3) = 1,000 liters (L)
2. Milliliter (mL) = 0.001 liters (L)
3. Centiliter (cL) = 0.01 liters (L)
4. Microliter (μL) = 0.000001 liters (L)
5. Liter (L) = 1 liter (L)
6. Deciliter (dL) = 0.1 liters (L)

Now, we will list them with the corresponding values in liters:

1. [tex]\( m^3: 1,000 \text{ liters} \)[/tex]
2. [tex]\( mL: 0.001 \text{ liters} \)[/tex]
3. [tex]\( cL: 0.01 \text{ liters} \)[/tex]
4. [tex]\( \mu L: 0.000001 \text{ liters} \)[/tex]
5. [tex]\( L: 1 \text{ liter} \)[/tex]
6. [tex]\( dL: 0.1 \text{ liters} \)[/tex]

We now organize these values from the largest to the smallest:

1. [tex]\( m^3: 1,000 \text{ liters} \)[/tex]
2. [tex]\( L: 1 \text{ liter} \)[/tex]
3. [tex]\( dL: 0.1 \text{ liters} \)[/tex]
4. [tex]\( cL: 0.01 \text{ liters} \)[/tex]
5. [tex]\( mL: 0.001 \text{ liters} \)[/tex]
6. [tex]\( \mu L: 0.000001 \text{ liters} \)[/tex]

Therefore, the order of the units from largest to smallest is:
[tex]\[ m^3, L, dL, cL, mL, \mu L \][/tex]

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