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Whether you like it or not, we use numbers every day.
不管你喜不喜歡，我們每天都會用到數字。
Some numbers, such as the speed of sound, are small and easy to work with.
有些數字比如音速，數值不大，容易計算。
Other numbers, such as the speed of light, are much larger and cumbersome to work with.
另一些數字，比如光速，就要大得多，不方便計算。
We can use scientific notation to express these large numbers in a much more manageable format.
我們能用科學計數法來表示它們，這樣的格式更容易進行操作。
So we can write 299,792,458 meters per second as 3.0 times 10 to the eighth meters per second.
那么我們可以把每秒299,792,458米，寫成每秒3.0乘10的8次方米。
Correct scientific notation requires that the first term range in value so that it is greater than one but less than 10, and the second term represents the power of 10 or order of magnitude by which we multiply the first term.
把第一項數值按照科學計數法改寫后，應該比1大但是比10小，而用來與第一項相乘的第二項的數值應該為10的次方數，或者叫數量級。
We can use the power of 10 as a tool in making quick estimations when we do not need or care for the exact value of a number.
運用10的次方就能迅速估算出我們只需了解其大約數值的數字。
For example, the diameter of an atom is approximately 10 to the power of negative 12 meters.
舉例來說，原子的直徑大約是10的負12次方米。
The height of a tree is approximately 10 to the power of one meter.
樹的高度大約是10的1次方米。
The diameter of the Earth is approximately 10 to the power of seven meters.
而地球的直徑大約是10的7次方米。
The ability to use the power of 10 as an estimation tool can come in handy every now and again, like when you're trying to guess the number of M&M's in a jar, but is also an essential skill in math and science, especially when dealing with what are known as Fermi problems.
把10的次方數當作估算工具有時能方便我們進行估算，例如，猜廣口罐里有幾顆M&M豆，而這也是解決數學和科學問題的必要技巧，尤其是在處理所謂的“費米問題”的時候。
Fermi problems are named after the physicist Enrico Fermi, who's famous for making rapid order-of-magnitude estimations, or rapid estimations, with seemingly little available data.
“費米問題”是以物理學家恩里科·費米的名字命名，他因為能利用一些看似極少的數據，迅速估算數量級和數字而聞名于世。
Fermi worked on the Manhattan Project in developing the atomic bomb, and when it was tested at the Trinity site in 1945,
費米在曼哈頓計劃中指導制造原子彈，1954年，進行三位一體試驗時，
Fermi dropped a few pieces of paper during the blast and used the distance they traveled backwards as they fell to estimate the strength of the explosion as 10 kilotons of TNT, which is on the same order of magnitude as the actual value of 20 kilotons.
費米在核爆途中扔下一些紙張，利用紙張往后落下的距離估算爆炸的威力，結論是相當于一萬噸的TNT，跟實際值的兩萬噸在同一個數量級。
One example of the classic Fermi estimation problems is to determine how many piano tuners there are in the city of Chicago, Illinois.
舉一個關于費米問題的經典例子：估算在伊利諾伊州的芝加哥有多少鋼琴調音師。
