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At first, there seem to be so many unknowns that the problem appears to be unsolvable.
乍一看存在太多未知的信息，這個問題根本無法回答。
That is the perfect application for a power-of-10 estimation, as we don't need an exact answer, an estimation will work.
這是運用10的次方數極好的例子，因為我們并不需要知道確切的數字——只要估算即可。
We can start by determining how many people live in the city of Chicago.
我們可以從估算芝加哥的人口開始。
We know that it is a large city, but we may be unsure about exactly how many people live in the city.
我們都知道芝加哥是一個很大的城市，但并不知道確切的人口數。
Are the one million people? Five million people?
一百萬人嗎？還是五百萬人？
This is the point in the problem where many people become frustrated with the uncertainty, but we can easily get through this by using the power of 10.
問題的重點在于很多人對這種不確定性感到棘手，而我們可以通過運用10的次方數輕易做到。
We can estimate the magnitude of the population of Chicago as 10 to the power of six.
我們估計芝加哥城人口大約是10的6次方。
While this doesn't tell us exactly how many people live there, it serves an accurate estimation for the actual population of just under three million people.
即使我們不知道確切的人數，但還是能了解其實際人數應該不會超過三百萬。
So if there are approximately 10 to the sixth people in Chicago, how many pianos are there?
如果芝加哥人口約有10的6次方，那會有多少鋼琴呢？
If we want to continue dealing with orders of magnitude, we can either say that one out of 10 or one out of one hundred people own a piano.
要是我們還想用數量級來處理，就可以估測，每10人或每100人就有一人擁有鋼琴。
Given that our estimate of the population includes children and adults, we'll go with the latter estimate, which estimates that there are approximately 10 to the fourth, or 10,000 pianos, in Chicago.
先前的人口估算包括大人和小孩，現在我們只算小孩的部分。那么芝加哥的鋼琴數約有10的4次方，差不多相當于1萬。
With this many pianos, how many piano tuners are there?
有這么多架鋼琴，那調音師到底有幾位呢？
We could begin the process of thinking about how often the pianos are tuned, how many pianos are tuned in one day, or how many days a piano tuner works, but that's not the point of rapid estimation.
可以從一架鋼琴多久調一次音，一天調幾架鋼琴，調音師工作幾天等等開始著手，但這不是快速預估的重點。
We instead think in orders of magnitude, and say that a piano tuner tunes roughly 10 to the second pianos in a given year, which is approximately a few hundred pianos.
我們在這里用數量級估算，一位調音師一年中，大約要為10的2次方架鋼琴調音，也就是差不多幾百架鋼琴。
Given our previous estimate of 10 to the fourth pianos in Chicago, and the estimate that each piano tuner can tune 10 to the second pianos each year, we can say that there are approximately 10 to the second piano tuners in Chicago.
先前估計出芝加哥的鋼琴約有10的4次方架，又估算了每位調音師一年可以替10的2次方架鋼琴調音，現在我們就可以說，芝加哥的調音師人數約有10的2次方這么多。
Now, I know what you must be thinking: How can all of these estimates produce a reasonable answer?
現在你一定在想：為什么這些預估都能算出合理的數字？
Well, it's rather simple.
答案再簡單不過。
In any Fermi problem, it is assumed that the overestimates and underestimates balance each other out, and produce an estimation that is usually within one order of magnitude of the actual answer.
每個費米問題都會假設高估和低估會彼此平衡，而其估計誤差通常只與其實際數值相差一個數量級。
In our case we can confirm this by looking in the phone book for the number of piano tuners listed in Chicago.
我們也可以用黃頁來確認這個例子中芝加哥到底有幾位調音師，
What do we find? 81.
有幾位呢？答案：81。
Pretty incredible, given our order-of-magnitude estimation.
數量級的估算方法很不可思議吧。
But, hey, that's the power of 10.
看，這就是10的力量。
