上面的高分答案完全正确。

首先，你的问题中混合了以2为底和以10为底的数，然后当你把一个不能整除的数放在右边时，你就有问题了。比如十进制的1/3因为3不能整除10的幂，或者二进制的1/5不能整除2的幂。

Another comment though NEVER use equal with floating point numbers, period. Even if it is an exact representation there are some numbers in some floating point systems that can be accurately represented in more than one way (IEEE is bad about this, it is a horrible floating point spec to start with, so expect headaches). No different here 1/3 is not EQUAL to the number on your calculator 0.3333333, no matter how many 3's there are to the right of the decimal point. It is or can be close enough but is not equal. so you would expect something like 2*1/3 to not equal 2/3 depending on the rounding. Never use equal with floating point.

上面的高分答案完全正确。

首先，你的问题中混合了以2为底和以10为底的数，然后当你把一个不能整除的数放在右边时，你就有问题了。比如十进制的1/3因为3不能整除10的幂，或者二进制的1/5不能整除2的幂。

Another comment though NEVER use equal with floating point numbers, period. Even if it is an exact representation there are some numbers in some floating point systems that can be accurately represented in more than one way (IEEE is bad about this, it is a horrible floating point spec to start with, so expect headaches). No different here 1/3 is not EQUAL to the number on your calculator 0.3333333, no matter how many 3's there are to the right of the decimal point. It is or can be close enough but is not equal. so you would expect something like 2*1/3 to not equal 2/3 depending on the rounding. Never use equal with floating point.

BCD -二进制编码的十进制-表示是精确的。它们不是很节省空间，但在这种情况下，这是为了准确性而必须做出的权衡。

你不能用二进制精确地表示0.1，就像你不能用传统的英国尺测量0.1英寸一样。

英国的尺子，就像二进制分数一样，都是关于一半的。你可以测量半英寸，或四分之一英寸(当然是一半)，或八分之一，或十六分之一，等等。

If you want to measure a tenth of an inch, though, you're out of luck. It's less than an eighth of an inch, but more than a sixteenth. If you try to get more exact, you find that it's a little more than 3/32, but a little less than 7/64. I've never seen an actual ruler that had gradations finer than 64ths, but if you do the math, you'll find that 1/10 is less than 13/128, and it's more than 25/256, and it's more than 51/512. You can keep going finer and finer, to 1024ths and 2048ths and 4096ths and 8192nds, but you will never find an exact marking, even on an infinitely-fine base-2 ruler, that exactly corresponds to 1/10, or 0.1.

不过，你会发现一些有趣的事情。让我们看看我列出的所有近似值，对于每一个近似值，明确地记录0.1是大是小:

现在，如果向下读最后一列，就会得到0001100110011。1/10的无限重复二进制分数是0.0001100110011，这不是巧合……

一个简单的答案是:计算机没有无限的内存来存储分数(在以科学记数法的形式表示十进制数之后)。根据IEEE 754双精度浮点数标准，我们只有53位的限制来存储分数。 欲了解更多信息:http://mathcenter.oxford.emory.edu/site/cs170/ieee754/

数字61.0确实有一个精确的浮点运算——但这并不是对所有整数都适用。如果您编写了一个循环，将一个双精度浮点数和一个64位整数都加了1，最终您将达到这样的情况:64位整数完美地表示一个数字，而浮点数却不能——因为没有足够的有效位。

只是在小数点右边求近似值要容易得多。如果你把所有的数字都写成二进制浮点数，这就更有意义了。

另一种思考的方式是，当你注意到61.0完全可以用10为底表示时，移动小数点并不会改变这一点，你是在执行10的幂乘法(10^1,10^-1)。在浮点数中，乘以2的幂并不影响数字的精度。试着用61.0反复除以3来说明一个非常精确的数字是如何失去它的精确表示的。