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Problem of the Week
Problem B and Solution
What’s in a Measure?

Problem

Listed below are measurements for some specific items. However, the unit of measure may not be what you are used to. Convert the measurements to a unit that makes more sense to you.

  1. The time between your \(10\)th and \(11\)th birthdays is \(31\,536\,000\) seconds.

  2. The distance between Montreal and Toronto is \(54\,160\,000\) centimetres.

  3. The length of my toothbrush is \(0.00019\) kilometres.

  4. I pour \(0.25\) litres of milk on my cereal in the morning.

Solution

  1. The time between your \(10\)th and \(11\)th birthdays is more commonly known as \(1\) year. (Hopefully, students did not need to do any calculations to determine this!) If you want to do the calculations, divide \(31\,536\,000\) by \(60\) to get \(525\,600\) minutes. Then divide \(525\,600\) by \(60\) to get \(8760\) hours. Finally, divide \(8760\) by \(24\) to get \(365\) days, which is equal to \(1\) year.

  2. A more reasonable unit for the distance between Montreal and Toronto is kilometres. So we will first convert the distance to metres and then to kilometres.

    That is, \(54\,160\,000\) cm is equal to \(54\,160\,000\div 100 = 541\,600\) m, and \(541\,600\div 1000=541.6\) km.

    Therefore, the distance between Montreal and Toronto is 541.6 km.

  3. A more reasonable unit for the length of my toothbrush would be centimetres. So we will first convert the length to metres and then to centimetres.

    That is, \(0.00019\) km is equal to \(0.00019\times 1000 = 0.19\) m, and \(0.19\times 100 =19\) cm.

    Therefore, the length of the toothbrush is \(19\) cm.

  4. A more reasonable unit for the amount of milk is millilitres. Therefore, the amount of milk is \(0.25\,\text{L}\times 1000=250\,\)mL.

Note: The units chosen may vary, since different students may find different units reasonable.