03 解释科学计数法 Explaining Scientific Notation

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Big numbers like this are cumbersome and difficult to read. Just watch all those zeros going by. Lots of them, aren't there?

If scientists had to read or write them out in full when they were discussing things like the molecules of water in a swimming pool or the distance to the Orion nebula, it would take up pages of books. The same is true of very small numbers like this one. And it's an important numberthe charge on a single electron.

But you could spend so much time counting the zeros you lose track of what the number was about. So, how do scientists solve the problem of very big and very small numbers?

In fact, scientists use a really simple device called scientific notation that allows them to abbreviate these numbers so that they're easy to write down and work with. The numbering system we use works in tens. That's the basis of our counting system.

So 2, 20, 200, and 2,000 are increasingly large numbers. They're also each 10 times larger than the previous number. You could think of that set of numbers as 2, 2 multiplied by 10, 2 multiplied by 100, and 2 multiplied by 1,000. But that doesn't help much for very large numbers.

The same numbers could also be written as 2, 2 times 10, 2 times 10 times 10, and 2 times 10 times 10 times 10. Think of that as 2, 2 times 10 one time, 2 times 10 two times, and 2 times 10 three times. Scientists write that with a superscript and describe it as 'to the power of'.

This last number is, therefore, 2 times 10 to the power three. This is scientific notation.

You can write any number like this, and they're all roughly the same length, even 2 times 10,100 times. The basic form of scientific notation is a number. Let's call this number A multiplied by 10 to the power of another number. Let's call this number B. B tells you how many times 10 shall be multiplied by itself.

Let's start with the number 500. You can visualize the process of scientific notation by focusing on the decimal point of the number and imagining it hopping over digits until there's only one digit left in front of it. Also, ​ note that the number left in front of the decimal needs to be greater than 0 and less than 10. This is an important point which we'll get to later.

So, for 500, the action number could also be written 5 times 10 times 10. Another way to think about that is that the decimal point is at the right-handend and it needs to hop over two digits until there's only one digit remaining in front of it. The number of hops is two, which is, therefore, the number B. So the number 500 is written as 5 times 10 to the power of 2 in scientific notation.

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