a decimal or a number is changed to a percent
I am not asking for the definition of percent
Too bad for you because I'm going to give you a definition (off the cuff), anyways!
Or, I hope, at least some new perspective for you.
Numbers do not really "change" into percents. We
interpret numbers as
percents, when we need a mechanism for calculating a percentage of some thing OR when we would like to make a statement of comparison between some whole thing and a fractional part of it.
A
percentage is a factional amount of some thing, expressed in terms of 100ths.
What is the meaning of "expressed in terms of 100ths"? Computationally (to me), it means taking that thing and dividing it up into 100 equal pieces, followed by counting the number of relevant pieces, in order to express the calculated percentage of the whole.
EG:
I desire to express the amount of water-damaged baseball cards in my collection as a percentage of the whole collection. For this example, it matters not how many cards make up the entire collection or what the actual percentage turns out to be. I'm trying to demonstrate "in terms of 100ths"
I sort the cards into two piles: one damaged, and the other not damaged. Then, I place the damaged pile on top of the undamaged pile, and start counting out the cards, to divide the entire collection into 100 equal-numbered groups.
So, the entire collection now sits on the table in 100 piles; each pile has the same number of cards.
The first 16 piles turn out to be damaged, and the remaining 84 piles are not damaged.
I express the damaged percentage as "16% of my collection".
Again, the expression
16% is a percent, a way to think about how the size of the damaged collection compares to the size of the whole collection. Most everybody can relate to the ratio 16:100 (compare 16 cents to 100 cents, how much of a dollar is that -- what can ya buy for 16 cents?). Hence, the expression "
16% of the thing" gives us a real sense of comparative size of the damaged part.
Of course, the expression 16% is also how we calculate actual numercial value for a percentage.
The percent sign % literally means "divide by 100". In this regard, symbol % may be thought of as a mathematical operator meaning: multiply by 1/100.
When you multiply some thing by 1/100, that's basically dividing the thing into 100 equal pieces, yes?
The number itself -- the one with the percent sign after it -- is the total number of those 100 equal pieces that make up the fractional part of the whole (in terms of 100ths because we already multiplied by 1/100).
In my example, let's now say that 3,200 cards comprise the collection. To calculate the percentage (the fractional part of the collection that's damaged) we multiply by 16%
16% * 3200 = 16 * 1/100 * 3200 = 16 * 3200/100
Dividing the collection into 100 equal groups yields piles containing 32 cards each. We now multiply by 16, to count out sixteen of the 32-card piles.
= 16 * 32 = 512
Now we know how many cards make up 16% of a 3,200-card collection.
Just as 16 cents is to $1, so is 512 cards to the whole 3,200.
Percentages are ratios.
Percents are numbers that we interpret as either a mechanism to calculate such percentages or as a ratio for comparison of how some fractional part of some thing compares to its whole.
0.16 is the decimal form of 16%
When we rewrite 0.16 as 16/100, we are not "changing" the number 0.16 into a percent; it was interpreted as a percent when we wrote it as 0.16 (specifically, the decimal form), and it is now interpreted as the same percent when we rewrite it as 16% (for expressing ratios) or 16/100 (for calculations).
I hope that you were able to follow most of that! (Read carefully; I misstatement stuff, from time to time.)
Cheers :cool:
