## Kiss those Math Headaches GOODBYE! ### How to Convert Percents to Decimals — Flawlessly

My last post showed how you convert decimals to percents.

Now I’ll dare to do the obvious with a post on how to convert percents to decimals.

Since converting percents to decimals is the opposite of converting decimals to percents, it makes sense — does it not? — that we’d use the opposite procedure. And that is the case. Not only that, but we do the opposite procedure in the opposite order, too. How’s that for going totally opposite?

Since the final step in converting decimals to percents is tacking on a percent symbol (%), the very first step in converting percents to decimals is taking off that symbol.

And since the first step in converting decimals to percents is nudging the decimal point two places to the right, the last step in converting percents to decimals is pushing the decimal point two places to the left.

Let’s take a look at the process with this example.

Problem:  convert 73.2% to a decimal.

Step 1:  Take off the percent symbol. 73.2% changes to just 73.2

Step 2:  Move the decimal point two places to the left. 73.2 changes to .732 That’s all there is to it. This tells us that 73.2% is the same as .732, or 7 hundred thirty-two thousandths.

If you don’t recall the steps that you’re turning around, here’s a quick way to remember the process of converting percents to decimals. As I said in my last post, we can make use of alphabetical order, setting up the words for decimal and percent, in order, like this:

D-Decimal                              P-Percent

Then we draw an arrow showing that we’re converting from percent form to decimal form. The arrow shows the direction of the conversion: percent to decimal.

D-Decimal    <————–    P-Percent

This arrow points to the left, and that tells us that we move the decimal point to the left when we convert a percent to a decimal.

Let’s look at the process again, this time focusing now on how we use the arrow’s direction to help us.

Problem:  Convert  4.782% to a decimal.

Step 1:  Rip off the percent symbol. 4.782% changes to 4.782

Step 2:  Give the decimal point two shoves in the arrow’s direction. Since a percent to decimal conversion makes the arrow point left, we shove the decimal point two spaces to the left.  4.782 changes to .04782

This tells us that .04782 is the same as 4.782%

Note: if there are no digits showing to the left, we’re free to add 0s on the left side of the leftmost digit to create a place where the decimal point lands, after being shoved to the left.

In the last example, we had to tack a 0 on the left of 4.782 — making it 04.782, to get a digit (0) to the left of which we placed the final decimal point. Be confident that you can write as many 0 digits as you need to the left of a number’s leftmost digit. For example, it is just fine (though admittedly strange) to write 4.3 as 0004.3. You’d do this weird maneuver if you need that many zeros to the left of the 4. This occurs in converting numbers to scientific notation, for example.

So, now that you know the process, try your hand at converting the following percents to decimals: (Answers at the bottom of this post.)

a)  38%                                                                                                                           b)  19.3%                                                                                                                         c)   4.2%                                                                                                                         d)  175%                                                                                                                         e)  398.6%
f)  2,400%

Answers to the problems in the last post, converting decimals to percents:

a)  8590%                                                                                                                     b)  416.2%                                                                                                                     c)  20873.5%
d)  4.7%
e)  207,465%
f)  28.3%
g)  .569%

Answers to problems in this post:

a)  38%        =  .38
b)  19.3%     =  .193
c)   4.2%      =  .042
d)  175%      =  1.75
e)  398.6%   =  3.986
f)  2,400%    =  24.0, or just 24

### How to Convert Decimals to Percents — Flawlessly

Math is filled with stuff you need to remember that’s hard to remember, right? Of course right.
So whenever we find a trick for math that’s helpful AND easy, we should learn it, right? Absolutely!

In that spirit, I’ld like to present a trick for converting decimals to percents. To learn the trick, you just need to think back to elementary school and remember alphabetical order. So just dust off the alphabet song you sang in kindergarten and join with me as we master the skill of converting decimals to percents.

First, notice that D comes before P in the alphabet.

So write these two letters in that order, D on the left (then some space), and P on the right, like so:

D                                     P

Next write the words, DECIMAL and PERCENT, after their first letters, like this:

D-DECIMAL                                    P-PERCENT

Now suppose you need to convert a decimal, such as .423, to its percent form. Can’t remember which way you move the decimal point? Eon’t sweat it because all you need to do is go back to your alphabetical diagram. Since we’re going from decimal form to percent form, draw an arrow that similarly goes from the word DECIMAL to the word PERCENT, like this:

D-DECIMAL   –––––––––––––––>     P-PERCENT

That arrow tells you which way to move the decimal point; since the arrow points to the right, you move the decimal point 2 places to the right. So you do this:

0.423 becomes 42.3

See how the decimal point “takes a little journey”? First the decimal point slips from between the 0 and the 4 to between the 4 and the 2. Then it sneaks over again, from between the 4 and the 2 to between the 2 and the 3. At this point you have the decimal point in the right spot, but there’s one last thing you need to do. Can you guess what it is … ?

O.K., here’s the answer: you tack a percent symbol (%) to the right of the right-most digit. So you take your 42.3 and put the % symbol to the right of the 3, like this:  42.3%.

What does this tell us? It says that 0.423 is equal to 42.3%.
As you’ve probably noticed, there are certain math rules that work some of the time but not all of the time. When they don’t work, people call those situations “exceptions,” and exceptions can be pretty annoying. But this decimal-to-percent trick works ALL OF THE TIME: no exceptions. So you can say it is 1.00 reliable (meaning, of course, 100% reliable). And that’s great. But before you try your hand at this skill, let’s check out one more example.

Suppose you’re asked to convert 5.1987 to a percent. Again the decimal point moves two places to the right. So first it slips from between the 5 and the 1 to between the 1 and the 9. Then it moseys to the right again, from between the 1 and the 9 to between the 9 and the 8. So at this point you have: 519.87. But don’t forget the important final step. Get out your “mental thumbtack” and tack a percent symbol after the right-most digit, the 7. So now you have the real answer:  519.87%.

And what does this mean? It tells us that 5.1987 is equal to 519.87%.