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The important thing about units is that once we've made a new unit, we can treat it just like we did the old unit.
重要的是，一旦我们创造了新的单位，就能用旧单位那样的方法使用它。
We can compose composed units, and we can partition partitioned units.
我们可以组成组合单位，也可以分成分割单位。
Think about toaster pastries.
想想看那些零食。
They come in packs of two, and then those packs get put together in sets of four to make a box.
它们两片包成一袋，然后再把四袋放在一起变成一盒。
So when I buy one box of toaster pastries, am I buying one thing, four things, or eight things?
所以我买一盒零食时，我是买了一个、四个、还是八个？
It depends on the unit.
这取决于单位。
One box, four packs, eight pastries.
一盒、四袋、八片。
And when I share a slice of pizza with a friend, we have to cut "it" into two smaller pieces.
当我跟朋友分享一片披萨时，我们必须将它切成更小的两片。
So a box of toaster pastries is composed of composed units, and when I split a slice of pizza, I'm partitioning a partitioned unit.
所以一盒零食是由一个组合单位组成的，而当我切开一片披萨时，我正在切出一个分割单位。
But what does that have to do with math?
但这些到底跟数学有什么关系？
In math, everything is certain.
数学中，所有东西都是确定的。
Two plus two equals four, and one is just one.
2加2等于4，1就是1。
But that's not really right.
但也不尽然。
One isn't always one.
1不一定永远是1。
Here's why: we start counting at one, and we count up to nine: 1,2,3,4,5,6,7,8,9, and then we get to 10, and in order to write 10, we write a one and a zero.
这就是原因：我们从1开始数一直数到9──1、2、3、4、5、6、7、8、9，接下来就数到10了，而为了写下10这个数字，我们写了一个1和一个0。
That one means that we have one group, and the zero helps us remember that it means one group, not one thing.
其中的1就表示我们有了一个群组，而0帮助我们记得它是指一组，而不是一个。
But 10, just like one, just like a dozen eggs, just like an egg, 10 is a unit.
但是10就像1、一打鸡蛋或一颗鸡蛋一样，是一个单位。
And 10 tens make 100.
而十个10就构成了100。
So when I think about 100, it's like the box of toaster pastries.
所以当我们在想100是什么的时候，它就像那一盒零食。
Is 100 one thing, 10 things or 100 things?
100是一个、10个或是100个东西？
And that depends on what "one" is, it depends on what the unit is.
这取决于那个“一”指什么，它的单位是什么。
So think about all the times in math when you write the number one.
所以碰到数学需要写一的时候，要一直想着这件事。
No matter what place that one is in, no matter how many things that one represents, one is.
不管这个一是放在哪个位置，不管这个一里有多少东西，它就是一。
