科学计数法(科学计数法的标准形式)

 

Big numbers like this are cumbersome and difficult to read. Just watch all those zeros going by. Lots of them, arent there?

像这样的大数字很麻烦，也很难读。只要看看后面跟着的所有这些零。非常多，不是吗？

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 its an important number—the charge on a single electron.

如果科学家在讨论游泳池里的水分子或距离猎户座星云的距离等问题时，必须完整地把它们全部读出来或写出来，就会占用好几页书。像这样非常小的数字也是如此。它是一个重要的数字——单个电子的电荷。

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?

但你可以花那么多的时间数零的个数，你会忘记这个数字是关于什么的。那么，科学家是如何解决非常大和非常小的数字问题的？

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

事实上，科学家们使用了一种非常简单的称为科学记数法的设备，它让科学家们可以缩写这些数字，以使这些数字易于记下和使用。我们使用的记数系统是十进制。这是我们计数系统的基础前提。

So 2, 20, 200, and 2,000 are increasingly large numbers. Theyre 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 doesnt help much for very large numbers.

因此，2，20，200和2000的数字是越来越大。它们每个数字都是前一个数字的十倍。你可以把这一组数字想象成 2，2 乘以 10，2 乘以 100，2 乘以1000。但这对非常大的数字而言帮助不大。

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.

同样的数字也可以写为 2，2乘以10，2 乘以10再乘以10，和2乘以10再乘以10再乘以10。可以认为是2，2乘以10一次，2乘以10两次，2乘以10三次。科学家们用上角标书写这些数字，并将其描述为 "次幂"。

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

这最后一个数字，因此，是2乘以10的3次幂。这就是科学计数法。

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

你可以用这种方法写任何数字，它们的长度都差不多，甚至是2乘以10乘以100次。科学记数法的基本形式是数字。让我们把这个数字称为 A 乘以10的另一个数字次的幂。让我们把另一个数字称为 B. B告诉你10应该乘以多少次本身。

Lets 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 theres 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 well get to later.

让我们从500这个数字开始。你可以通过关注数字的小数点并想象它跳过数字直到它前面只剩下一个数字，来可视化科学记数法的过程。另请注意，小数前面留下的数字必须大于0且小于10。这是我们稍后会介绍的重点。

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-hand​ end and it needs to hop over two digits until theres 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.

因此，对于500，数字运算也可以写5乘以10再乘以10。另一种思考方式是，小数点在右手端，它需要跳过两位数字，直到前面只剩下一个数字。跳跃的点数为2，也就是数字B。所以用科学计数法写数字500，则写为5乘以10的2次幂。

How about writing the number 7,500 in scientific notation? This time, the decimal point hops over three digits so the number B is a 3. If we remove the zeros that the decimal point hopped over, were left with 7.5. So the number A is replaced by 7.5. The number 7,500, can be written in scientific notation as 7.5 times 10 to the power of 3.

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用科学记数法写7500怎么样？这一次，小数点跃过三位数，所以数字 B 是3。如果我们删除小数点跳过的零，我们就剩下7.5。因此，数字 A 被7.5 替换。这个数字，7500，可以用科学计数法写成7.5 乘以10的3次幂。

We can check that this is correct by working out the individual components. 10 times 10 times 10 equals 1,000. And 7.5 times 1,000 gives us our original number of 7,500.

我们可以通过计算各个部分来检查这是否正确。10乘以10乘以10等于1000。7.5乘以 1000 就是我们原来的数字7500。

Small numbers can be written in a very similar way. Lets start with the number 0.05.

小数字可以用非常相似的方式书写。让我们从数字0.05开始。

The only number here greater than 0 is the 5 at the right hand end of the number. This means that the decimal point needs to hop over digits to the right until the 5 is in front of it. To do this, the decimal point hops over two numbers. Again, the number B is replaced by a 2.

这里唯一大于0的数字是数字右侧的5。这意味着小数点需要向右跳过数字，直到5在它前面。为此，小数点将跃过两个数字。同样，数字 B被2替换。

However, because weve moved towards the right, were moving toward smaller numbers. And therefore, a minus sign is required before the 2. If we remove all the zeros that we hopped over and the one that was before the decimal place, were left with the number 5. This becomes our number A. So the number 0.05 can be written in scientific notation as 5 times 10 to the power of minus 2.

然而，因为我们已经向右边移动了，我们正朝着较小的数字移动。因此，在2之前需要一个减号。如果我们删除了我们跳过的所有零和小数位之前的那个零，我们只剩下数字5。这就成了我们的数字A。所以数字0.05可以用科学记数法写成，5乘以10的-2次幂。

Again, we can check that this is correct by working out the individual components. 10 to the power of minus 2 is actually 0.1 times 0.1 which equals 0.01. And 0.01 multiplied by 5 results in 0.05.

同样，我们可以通过计算各个部分来检查这是否正确。10的-2次幂实际上是 0.1乘以0.1等于0.01。0.01 乘以5结果是0.05。

You should now be able to write our original very large number and very small number in scientific notation. For the large number, the decimal point hops over 22 digits and is left with a 1 in front of it.

你现在应该能够用科学计数法书写我们最开始非常大的数字和非常小的数字。对于大数字，小数点跳过22位数，前面剩下一个1。

Dont worry, you wont have to do this very often. Most numbers like this are normally already written in scientific notation.

别担心，你不必经常这样做。像这样的大多数数字通常已经是用科学计数法书写的了。

In scientific notation, this number is 1 times 10 to the 22. For the very small number, the decimal point needs to hop right over 19 digits and leaves us with 1.6.

在科学记数法中，这个数字是1乘以10的22次幂。对于非常小的数字，小数点需要直接跳过19位数字，给我们留下了1.6。

In scientific notation, this is written as 1.6 times 10 to the minus 19, which is the electric charge of a single electron. Its an important number thats much easy to remember in scientific notation.

在科学计数法中，这被写成1.6 乘以10的-19次幂，即单个电子的电荷。这是一个重要的数字，在科学计数法中很容易被记住。

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