What Is Percent?

The word percent is of Latin lineage:

percent (noun), percentage (noun): the first component is from Latin per "for." The Indo-European root is per- "forward, through, in front of," and many other things. The second component is from Latin centum "hundred," from the Indo-European root dekm-tom-, a form of dekm- "ten," because a hundred is ten tens. The word percent means literally "for (each) hundred." In older American books the full Latin phrase per centum was normally used. Later the abbreviation per cent. appeared, and eventually the period after the last letter was dropped. Modern usage allows percent as one word or per cent as two words. The symbol that commonly represents percent, %, may have originated from the second part of p c°, an early Italian abbreviation of per cento. By the 17th century the symbol o/o was in common use in Europe to represent a percent. In any case, the current symbol, with its two "zeros," is a convenient reminder that a percent is a fraction whose denominator, 100, also contains two zeros.

So one percent is simply one hundredth, 1% = 1/100, n% = n/100. Oftener than other fractions, percents are percents of something, of another quantity. For example, 5% of 120 is 120×5/100 = 6. A penny is 1%, a nickel 5%, a dime 10% and a quarter 25% of a dollar.

To grow by 100% means to become twice as big, because a 100% growth means adding 100% of what was already there another 100% to the total of 200%. Losing 100% means losing everything.

Assume, your stock in a XYZ company lost 20% of its value. It might have been, for example, worth $1000 and by losing 20% (which is 1000×20/100 = 200) has the current worth of $800. What does it take to get you money back? In other words, now starting at $800, how much (in percents) you should gain so that your stock is back to its original value of $1000? Do you think that, since your lost 20%, all it takes to get back to $1000 is to gain your 20% back? Well, it is not so.

Obviously, to make your stock worth the original $1000, you should gain the lost $200. But $200 is now a portion of your current holdings of $800, and is such is not 20% of the latter. (20% of $800 equal $800×20/100 = $160.) So what portion of $800 is the amount of $200? It's 1/4, of course. In terms of percents, seek a fraction equal to 1/4 with the denominator of 100: 1/4 = 25/100 = 25%.) So, here is a lesson to learn: it is easier to lose money than to gain some.

Percents provide a relative view of quantitative information. For example, it is known that, in the year 2000 elections, Ralph Nader received more votes (2,800,000) than did Lincoln (1,900,000) in 1860. However, in 1860 there were less than 5000000 eligible voters while in 2000 their number exceeded 100000000. Turning to percents, Nader received 2800000/100000000×100% = 2.8%, whereas Lincoln received a whooping 1900000/5000000×100% = 38%.

[A. K. Dewdney, pp. 9] tells an amazing anecdote

A man by the name of Smith was walking home from work when he spotted a $5 bill on the pavement. He looked around, picked it up, and put it in his pocket. His other pocket already contained a $10 bill. Smith smiled. "My wealth has increased by 50 percent," he said to himself.

Unfortunately, the pocket that held the $5 bill had a hole in it. When Smith got home, he discovered to his dismay that the $5 was missing. "That's not so bad," he said. "Earlier, my wealth increased by 50 percent, now it has decreased by only 33 percent. I'm still ahead by 17 percent!"

Here's an interesting problem [Crimes and Mathdemeanors, pp. 21-26]: a watermelon is 99% water. As one would expect, if a watermelon left under the sun, it loses some of its water contents (and, hence, some of its weight) to evaporation. Assume, that after a while water constitutes 98% of its remaining weight. How much of weight (in percents) has been lost?

Give it a thought before reading further.

Note: percent is the most fundamental part of the interest (on loan, mortgage) calculations.

References

  1. A. K. Dewdney, 200% of Nothing, John Wiley & Sons, Inc., 1993
  2. L. Hathout, Crimes and Mathdemeanors, A K Peters, 2007
  3. D. Niederman, D. Boyum, What the Numbers Say, Broadway Books, 2003, p. 79
  4. S. Schwartzman, The Words of Mathematics, MAA, 1994

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    Copyright © 1996-2017 Alexander Bogomolny

    A surprise: it's not 1% (99% - 98%) but a tremendous 50%! How do you figure that? If originally the watermelon was 99% water, then the chewy part was just 1%. The same quantity became 2% (= 100% - 98%) of a shrunk watermelon. Say, if the original watermelon weighted 10 pounds, the chewy part weighted 10×1/100 = 1/10 lb. What is the quantity of which 1/10 is 2%? Let it be x. Then x×2/100 = 1/10, from which x = 1/10 ÷ 2/100 = 1/10 ×100/2 = 50! The shrunk watermelon now weights only 5lb which is 50% of the original 100lb. The other 50% (all water) got lost to the elements.

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