How many water drops are there in the ocean?

First of all we have to pay attention that the word “drop” does not refer to any measurement Unit. Therefore, and because of the water cycle, the amount of water in the oceans is not always the same. Rivers are constantly flowing into the sea and there is a constant evaporation. Even so, from a mathematical point of view, we do not aim at obtaining an accurate answer to this question. Our aim is to get an acceptable approach. The most important point of these questions is leading the pupil to reflect and think about an approach to the problem as well as trying to reach a close answer through a mathematical reasoning. Asking how many drops there are in the ocean is the same of asking how many sand grains there are on the beaches. Or else: how many leaves are there in trees? How many people can play the piano around the world? How many tennis balls can I put in my classroom? No matter what the case is, the aim is always the same: motivating pupils to think.

But, after all, is there any way of knowing the answers?

Yes, there is. To start with, we can admit that a water drop corresponds to 0.05ml. It is the same of saying that 1 litre of water contains closely to 20,000 drops. At the moment we are faced with another problem: how many litres of water are there in the ocean? The following logical step would be useful to calculate the ocean volume. It is not easy because the depth is not always the same and besides that the sea coasts are very irregular. We can try an approach by searching the Google that will allows us to discover that the estimate for the oceans volume is about 1335 millions of cubic kilometres, having in mind that 70% of our Planet’s surface is water. To know how many litres there are we will use an equivalence which we are taught during the Primary school: `1 liter = 1 dm^3`. After some mathematical calculations, we arrive to the conclusion that oceans are formed by `2.67xx10^25` drops, which corresponds to the number 267 followed by 23 zeros!

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