Metric Units of Length Conversion

Solution to Example 3

Using the factors from Table 1 above going from \( \text{cm} \) to \( \text{dam} \), we write:

which gives the factors of conversion:

and

We are given \( \text{dam} \); we therefore use the factor of conversion (II) since it has \( \text{dam} \) in the denominator which may be cancelled.

Convert \( 170 \; \text{dam} \) as follows:

Cancel \( \text{dam} \):

Simplify:

Evaluate:

Solution to Example 4

Using the factors from \( \text{mm} \) to \( \text{hm} \) in Table 1 above, we write:

which gives the factors of conversion:

and

We are given \( \text{mm} \) which needs to be canceled; we therefore use the factor of conversion (I) because it has \( \text{mm} \) in the denominator.

Convert \( 12,500 \; \text{mm} \) as follows:

Cancel \( \text{mm} \) on the right:

Simplify:

Evaluate:

Solution to Example 5

Using the factors Table 1 above from \( \text{nm} \) to \( \text{cm} \), we write:

which gives the factors of conversion:

and

We are given \( \text{cm} \) which needs to be canceled, and we therefore use the factor of conversion (II) because it has \( \text{cm} \) in the denominator.

Convert \( 0.0023 \; \text{cm} \) as follows:

Cancel \( \text{cm} \) on the right:

Simplify:

Evaluate:

Solution to Example 6

Using the factors Table 1 above from \( \mu\text{m} \) to \( \text{hm} \), we write:

which gives the factors of conversion:

and

We are given \( \mu\text{m} \) which needs to be canceled, and we therefore use the factor of conversion (I) because it has \( \mu\text{m} \) in the denominator.

Convert \( 890,000 \; \mu\text{m} \) as follows:

Cancel \( \mu\text{m} \):

Simplify:

Evaluate:

Solutions to the Above Exercises

Part A

1. Convert \( 0.0102 \text{ Mm} \) to \( \text{hm} \).

   From Table 1, we have \( 1 \text{ Mm} = 10 \times 1000 \text{ hm} = 10,000 \text{ hm} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ Mm}}{10,000 \text{ hm}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{10,000 \text{ hm}}{1 \text{ Mm}} = 1 \quad (II) \]

   Use factor (II) because it has \( \text{Mm} \) in the denominator and we are converting \( \text{Mm} \):

   \[ 0.0102 \text{ Mm} \times \frac{10,000 \text{ hm}}{1 \text{ Mm}} = \frac{0.0102 \times 10,000}{1} \text{ hm} \]
   \[ 0.0102 \text{ Mm} = 102 \text{ hm} \]



2. Convert \( 0.3 \text{ nm} \) to \( \text{mm} \).

   From Table 1, we have \( 1 \text{ mm} = 1000 \times 1000 \text{ nm} = 1,000,000 \text{ nm} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ mm}}{1,000,000 \text{ nm}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{1,000,000 \text{ nm}}{1 \text{ mm}} = 1 \quad (II) \]

   Use factor (I) because it has \( \text{nm} \) in the denominator and we are converting \( \text{nm} \):

   \[ 0.3 \text{ nm} \times \frac{1 \text{ mm}}{1,000,000 \text{ nm}} = \frac{0.3 \times 1}{1,000,000} \text{ mm} \]
   \[ 0.3 \text{ nm} = 0.0000003 \text{ mm} \]



3. Convert \( 1200 \text{ m} \) to \( \text{Mm} \).

   From Table 1, we have \( 1 \text{ Mm} = 10 \times 10 \times 10 \times 1000 \text{ m} = 1,000,000 \text{ m} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ Mm}}{1,000,000 \text{ m}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{1,000,000 \text{ m}}{1 \text{ Mm}} = 1 \quad (II) \]

   Use factor (I) because it has \( \text{m} \) in the denominator:

   \[ 1200 \text{ m} \times \frac{1 \text{ Mm}}{1,000,000 \text{ m}} = \frac{1200 \times 1}{1,000,000} \text{ Mm} \]
   \[ 1200 \text{ m} = 0.0012 \text{ Mm} \]



4. Convert \( 13200 \text{ dm} \) to \( \text{km} \).

   From Table 1, we have \( 1 \text{ km} = 10 \times 10 \times 10 \times 10 \text{ dm} = 10,000 \text{ dm} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ km}}{10,000 \text{ dm}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{10,000 \text{ dm}}{1 \text{ km}} = 1 \quad (II) \]

   Use factor (I) because it has \( \text{dm} \) in the denominator:

   \[ 13200 \text{ dm} \times \frac{1 \text{ km}}{10,000 \text{ dm}} = \frac{13200 \times 1}{10,000} \text{ km} \]
   \[ 13200 \text{ dm} = 1.32 \text{ km} \]



5. Convert \( 0.002 \text{ Gm} \) to \( \text{km} \).

   From Table 1, we have \( 1 \text{ Gm} = 1000 \times 1000 \text{ km} = 1,000,000 \text{ km} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ Gm}}{1,000,000 \text{ km}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{1,000,000 \text{ km}}{1 \text{ Gm}} = 1 \quad (II) \]

   Use factor (II) because it has \( \text{Gm} \) in the denominator:

   \[ 0.002 \text{ Gm} \times \frac{1,000,000 \text{ km}}{1 \text{ Gm}} = \frac{0.002 \times 1,000,000}{1} \text{ km} \]
   \[ 0.002 \text{ Gm} = 2000 \text{ km} \]



6. Convert \( 13200 \; \mu\text{m} \) to \( \text{dm} \).

   From Table 1, we have \( 1 \text{ dm} = 1000 \times 10 \times 10 \; \mu\text{m} = 100,000 \; \mu\text{m} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ dm}}{100,000 \; \mu\text{m}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{100,000 \; \mu\text{m}}{1 \text{ dm}} = 1 \quad (II) \]

   Use factor (I) because it has \( \mu\text{m} \) in the denominator:

   \[ 13200 \; \mu\text{m} \times \frac{1 \text{ dm}}{100,000 \; \mu\text{m}} = \frac{13200 \times 1}{100,000} \text{ dm} \]
   \[ 13200 \; \mu\text{m} = 0.132 \text{ dm} \]



7. Convert \( 0.003 \text{ dam} \) to \( \text{mm} \).

   From Table 1, we have \( 1 \text{ dam} = 10 \times 10 \times 10 \times 10 \text{ mm} = 10,000 \text{ mm} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ dam}}{10,000 \text{ mm}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{10,000 \text{ mm}}{1 \text{ dam}} = 1 \quad (II) \]

   Use factor (II) because it has \( \text{dam} \) in the denominator:

   \[ 0.003 \text{ dam} \times \frac{10,000 \text{ mm}}{1 \text{ dam}} = \frac{0.003 \times 10,000}{1} \text{ mm} \]
   \[ 0.003 \text{ dam} = 300 \text{ mm} \]



8. Convert \( 0.001 \text{ cm} \) to \( \text{nm} \).

   From Table 1, we have \( 1 \text{ cm} = 1000 \times 1000 \times 10 \text{ nm} = 10,000,000 \text{ nm} \).

   Factors of conversion:

   \[ \displaystyle \frac{1 \text{ cm}}{10,000,000 \text{ nm}} = 1 \quad (I) \quad \text{or} \quad \displaystyle \frac{10,000,000 \text{ nm}}{1 \text{ cm}} = 1 \quad (II) \]

   Use factor (II) because it has \( \text{cm} \) in the denominator:

   \[ 0.001 \text{ cm} \times \frac{10,000,000 \text{ nm}}{1 \text{ cm}} = \frac{0.001 \times 10,000,000}{1} \text{ nm} \]
   \[ 0.001 \text{ cm} = 10,000 \text{ nm} \]