## Exercise - units and conversions

### Worked Exercises

- Write conversion factors for the following units:

a) Litres and millilitres

b) Ounces and grams.

a) \(1L=1000ml\)

\(\frac{1L}{1000g}\) and \(\frac{1000g}{1L}\)

b) \(1oz=28.3g\)

\(\frac{1oz}{28.3g}\) and \(\frac{28.3g}{1oz}\)

- Convert \(3.500lb\) pounds to grams (\(1lb=454g\)).

Relationship between two units - \(1lb=454g\)

Conversion factors - \(\frac{1lb}{454g}\) and \(\frac{454g}{1lb}\)

Only one of these conversion factors is required to convert pounds to grams. The conversion factor, \(\frac{454g}{1lb}\) , is required as it allows for the cancellation of the pound units, leaving gram as the new unit.

\( \frac{454g}{1lb}\times3.500lb=1589g \)

#### Exercises

**Write the conversion factors for the following:**

1. Centimetres and metres

\(1m = 100cm \)

\(\frac{1m}{100cm}\: \textrm{and} \frac{100cm}{1m} \)

2. micromoles and moles

\(1mol = 10^{-6}\mu mol \)

\(\frac{1mol}{10^{-6}\mu mol}\: \textrm{and} \frac{10^{-6}\mu mol}{1mol} \)

3. litres and gallons (\(1L=0.265gal\))

\(1L = 0.265gal \)

\(\frac{1L}{0.265gal}\: \textrm{and} \frac{0.256gal}{1L} \)

4. microlitres and millilitres

\(1000\mu L = 1mL \)

\(\frac{1000\mu L}{1ml}\: \textrm{and} \frac{1ml}{1000\mu L} \)

**Convert**

1. \(2.56gal\) gallons to litres (\(1L=0.265gal\))

\(\frac{1L}{0.265gal}\times2.65gal=10.0L\)

2. \(250.0mg\) to grams

\(\frac{1g}{1000mg}\times250.0mg=0.2500g\)

3. \(750.0\mu mol\) to millimoles

\(\frac{1mmol}{1000\mu mol}\times750.0\mu mol=0.7500\)

4. \(0.567ml\) to microlitres

\(\frac{1000\mu l}{1ml}\times0.567ml=567\mu L\)

5. Convert 45 km/h to m/s

12.5 m/s

6. Convert 26 m/s to km/h

93.6 km/h