609th post: When not to round off numbers

You come across a number that looks something like
and wonder how to round that off. Most people would just simply say 30 million or 25 million. Sometimes, however, knowing what the exact number can be important. Makes a difference when over/under estimation is involved, but when it comes to just talking to people about how big the number is, saying this can be quite a mouthful.

Anyway, I'm here to talk about rounding off numbers that you would come across for money. Before I go on, note that some countries uses "." or a space to separate 3 digits of whole numbers, and "," for decimals. For countries like India, the first group contains 3 digits, but subsequent groups contain only 2 digits.

Situations where you are more likely to come across more than 2 decimal places for money (or, depending on currency, trailing digits that are more than the lowest denomination) when calculating taxes or dealing with foreign currency. Here's an example of dealing with one:


In this case you could just simply round it off as "56.86" (57 or 60 if you are lazy). However, because of a "6" after the "4", it would be rounded off as "56.865". The problem here is that if you never saw the longer version, you would round it off to 2 digits as "56.87" instead of "56.86". A small increase, but if multiplied many times, it can make a big difference.

To put it in perspective, it's like measurements of a furniture part: you need it to be just right. A little more, and it would not fit. A little less, and it would not hold there and drop.

Need a math sum to see a bigger picture? Here's one with both exact and rounded numbers
56.86469×100000 = 5686469
57×100000 = 5700000
The difference between the two numbers is 13531. A difference that can make a lot of changes.


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