Convert measurement units

Length

\(\displaystyle 3.4\text{ m}\)

Convert the measured length to centimetres

A big unit is k small units long. Each grid cell is one small square unit. Move k and count the cells covered by the outlined square. The cube count is shown in the readout

Which rule matched the counts at every position of the slider?

Convert units with powers

A length uses the factor once, an area uses it twice and a volume uses it three times, because each dimension converts separately. Multiply when moving to a smaller unit and divide when moving to a larger unit

1. 1Match the direction Multiply when changing to a smaller unit, which needs a larger number. Divide when changing to a larger unit \(\displaystyle 4\text{ m}=(4\times100)\text{ cm}=400\text{ cm}\)
2. 2Use one factor for length A length has one dimension, so apply the length conversion factor once \(\displaystyle 1\text{ m}=100\text{ cm}\)
3. 3Square the factor for area An area has two length dimensions, so the factor is used twice \(\displaystyle \begin{gathered}0.6\text{ m}^2=(0.6\times100^2)\text{ cm}^2 \\ =6000\text{ cm}^2\end{gathered}\)
4. 4Cube the factor for volume A volume has three length dimensions, so the factor is used three times \(\displaystyle \begin{gathered}1\text{ m}^3=100^3\text{ cm}^3 \\ =1{,}000{,}000\text{ cm}^3\end{gathered}\)

Lawn area

\(\displaystyle 45\text{ m}^2\)

Convert the lawn area to square centimetres

Square the length factor for an area, then multiply because square centimetres are smaller than square metres

Soil volume delivered

\(\displaystyle 1{,}200{,}000\text{ cm}^3\)

Convert the delivered soil volume to cubic metres

Cube the length factor for a volume, then divide because cubic metres are larger than cubic centimetres

Volume and capacity

Cubic units measure volume. Litres and millilitres measure capacity; use these exact links when converting

1. 1Small capacity One cubic centimetre corresponds to one millilitre \(\displaystyle 1\text{ cm}^3=1\text{ mL}\)
2. 2Litres A thousand millilitres make one litre \(\displaystyle 1000\text{ cm}^3=1\text{ L}\)
3. 3Cubic metres A cubic metre holds one thousand litres \(\displaystyle 1\text{ m}^3=1000\text{ L}\)

Area

\(\displaystyle 7\text{ m}^2\)

Where is the first error in the area conversion?