## Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!

Navya asks: "Why do we have names for numbers?"

There are two answers to this question. The first answer is: because it's impossible to talk about numbers verbally unless you have names for them. If we didn't have the names "one", "two", "three" and so forth, how would we ever say "I have five apples"?

That explanation is sufficient for why we have names for the numbers from zero to nine, but it's not sufficient for numbers like eleven, twelve, and so on. After all, if we didn't have the name "eleven", we could still say the number by saying "one one."

Thus, we would count like this (starting at ten): "one zero, one one, one two, one three..." and so forth.

And in some cases, that would be quicker. The name "eleven" has three syllables, while "one one" just has two. Even worse would be a number like "three thousand, four hundred, sixty three" which takes nine syllables instead of the four syllables required for "three four six three".

So, since the number names aren't always quicker to say than just reciting off the digits, why do we bother? The answer is that using number names allows us to get an immediate order-of-magnitude sense for how big the number is. Look at it this way - if I say "seven million, two hundred twenty three thousand, four hundred twelve," the moment I said "seven million" you had a very good sense for how big that number is. But if instead I had said "seven two two three four one two" you would not have any way of determining the number's magnitude until I was all done reciting the digits, and you knew how many digits there were. And if you lost track of how many digits there were, youÂ *stillÂ *wouldn't have a good sense for how big the number is!

So number names are very helpful for order-of-magnitude sense of the size of a number.