# 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.