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

Practice

1. Convert the following:
   1. 250 metres ([latex]250 \text{ m}[/latex]) to kilometres.
      Answer:
      [latex]0.250~\text{km}[/latex]
   2. kilometres ([latex]178 \text{ km}[/latex]) to metres.
      Answer:
      [latex]178{,}000~\text{m}[/latex]
   3. 830 centimetres ([latex]830 \text{ cm}[/latex]) to metres.
      Answer:
      [latex]8.30~\text{m}[/latex]
   4. 375 centimetres ([latex]375 \text{ cm}[/latex]) 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]30 \times 10^{-6}~\text{dam}^3 = 3.0 \times 10^{-5}~\text{dam}^3[/latex]
3. Convert the following:
   1. [latex]1 \text{ in} \text{ = } 2.54 \text{ cm}[/latex]. Convert [latex]12 \text{ in}[/latex] into centimetres.
      Answer:
      [latex]30.48~\text{cm}[/latex]
   2. Convert [latex]3.5 \text{ m}[/latex] into inches.
      Answer:
      [latex]137.795~\text{in}[/latex]
   3. [latex]1 \text{ ft} \text{ = } 12 \text{ in}[/latex]. Convert [latex]23 \text{ ft}[/latex] into inches.
      Answer:
      [latex]276~\text{in}[/latex]
   4. Convert [latex]4 \text{ ft}[/latex] into [latex]\text{m}[/latex].
      Answer:
      [latex]1.2192~\text{m}[/latex]
4. Convert the following:
   1. [latex]72 \text{ km/h}[/latex] in [latex]\text{m/s}[/latex]
      Answer:
      [latex]20~\text{m/s}[/latex]
   2. [latex]5 \text{ m/s}[/latex] in [latex]\text{km/h}[/latex]
      Answer:
      [latex]18~\text{km/h}[/latex]
5. Convert the speed:
   1. Convert the speed [latex]\text{v = } 23 \text{ in/min}[/latex] to a speed expressed in [latex]\text{m/s}[/latex]. ([latex]1 \text{ in = } 2.54 \text{ cm}[/latex])
      Answer:
      [latex]0.00973667~\text{m/s}[/latex]
6. Convert the torque:
   1. [latex]76.5 \text{ lbs x ft}[/latex] to a torque expressed in [latex]\text{N x m}[/latex]. ([latex]1 \text{ ft = } 12 \text{ in}[/latex]; [latex]1 \text{ lb = } 4.45 \text{ N}[/latex])
      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.