1.3. Practice Sets: Units and Unit Conversions; Systems of Measurement

Practice

1. Convert the following:
   1. 250 metres (250 m) to kilometres.
      Answer:
      [latex]0.250~\text{km}[/latex]
   2. kilometres (178 km) to metres.
      Answer:
      [latex]178{,}000~\text{m}[/latex]
   3. 830 centimetres (830 cm) to metres.
      Answer:
      [latex]8.30~\text{m}[/latex]
   4. 375 centimetres (375 cm) to mm.
      Answer:
      [latex]3750~\text{mm}[/latex]
2. Convert the following:
   1. 2 square metres to square decimetres.
      Answer:
      [latex]2 \times 10^{2}~\text{dm}^2[/latex]
   2. 45 square centimetres to square metres.
      Answer:
      [latex]45 \times 10^{-4}~\text{dm}^2[/latex]
   3. 7 cubic metres to cubic decameters.
      Answer:
      [latex]7 \times 10^{-3}[/latex]
   4. 30 cubic decimetres to cubic decametres.
      Answer:
      [latex]\small 30 \times 10^{-6}~\text{dam}^3 = 3.0 \times 10^{-5}~\text{dam}^3[/latex]
3. Convert the following:
   1. 1 in = 2.54 cm. Convert 12 in into centimetres.
      Answer:
      [latex]30.48~\text{cm}[/latex]
   2. Convert 3.5 m into inches.
      Answer:
      [latex]137.795~\text{in}[/latex]
   3. 1 ft = 12 inches. Convert 23 ft into inches.
      Answer:
      [latex]276~\text{in}[/latex]
   4. Convert 4 ft into m.
      Answer:
      [latex]1.2192~\text{m}[/latex]
4. Convert the following:
   1. 72 km/h in m/s
      Answer:
      [latex]20~\text{m/s}[/latex]
   2. 5 m/s in km/h
      Answer:
      [latex]18~\text{km/h}[/latex]
5. Convert the speed:
   1. Convert the speed v = 23 in/min to a speed expressed in m/s. (1 in = 2.54 cm)
      Answer:
      [latex]0.00973667~\text{m/s}[/latex]
6. Convert the torque:
   1. 76.5 lbs x ft to a torque expressed in N x m. (1 ft = 12 in; 1 lb = 4.45 N)
      Answer:
      [latex]103.76~\text{N} \cdot \text{m}[/latex]
7. Imagine a trapezoidal garden with a base length of 12 metres, a top length of 8 metres, and a height of 5 metres. The garden has two parallel sides, where the longer side measures 12 metres and the shorter side measures 8 metres. The height of the garden, representing the distance between the two parallel sides, is 5 metres. Calculate the area in square metres, then covert to square feet.
   Answer:
   50 square metres, 538.2 square feet
8. Imagine a cube with a side length of 4 metres and a rectangular prism with dimensions 6 metres (length), 3 metres (width), and 2 metres (height) connected to form a playing structure. Calculate the volume of the structure in cubic metres, and then convert it to cubic feet
   Answer:
   100 cubic metres, 3531.47 cubic feet.