Percent
Fractions can be expressed in 3 different ways: ratios (fractions), decimals, or percents. Percents provide a convenient way to express a ratio because they tell you how many items are given per 100. The word percent (per + cent) means per 100. The symbol % looks like its meaning /100. |
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Suppose we have a half, 1/2. How do we write this as a percent? Well, you might already know that the answer is 50%, but how could we find this out if we didn't already know this? The key lies in the fact that % means per 100. We want to express 1/2 as some quantity out of 100. We can write this relationship as a proportion: 1/2 = ?/100. To solve this, we could cross multiply and divide to find the unknown. (1 × 100) ÷ 2 = 50. So 1/2 = 50/100 or 50%.
Let's look at a more difficult example. How do we write 1/3 as a percent? The proportion we need to solve is: 1/3 = ?/100.
We can cross multiply to solve. Take 1 ×
100. Then we take the product, 100, and divide by 3.
carrying it out
further, we get:
. As
you can see, the 3's keep repeating forever, so it will be easier to write 100/3
as a fraction by taking the remainder 1 and putting it over the divisor 3. Now
we get 33 1/3. So 1/3 = 33 1/3%.
So let's recap what we did here. Basically, we ended up taking 100 times the numerator divided by the denominator. We can summarize this procedure more simply as:
To write a fraction as a percent:
For example, 2/5 = .4 = 40%
Remember, you can replace the % symbol in any problem with /100.
For example, 50% can be written 50/100 by replacing the % symbol with
/100.
So 50% = 50/100 which reduces to 1/2. Well, OK, you might have already known
this.
Now, let's look at a trickier one. What is 11 1/9%? Replacing % with /100 we get that 11 1/9% = (11 1/9)/100. This is the same as 11 1/9 ÷ 100. If we invert & multiply, we have 11 1/9 ×1/100. Multiplying mixed numbers entails converting them to improper first, so wrote 11 1/9 as 100/9. Now we have 100/9 •1/100 which gives the product of 1/9. In other words, 11 1/9% = 1/9.
To summarize, we have just found a way to write any percent as a fraction by replacing % with /100.
To write any percent as a fraction:
For example, 40% = 40/100 = 4/10 = 2/5.
Percent, %, means divide by 100. This is the same as multiplying by 1/100 or .01. Recall that multiplying by .01 has the effect of moving the decimal 2 places to the left. E.g., 38% = 38 × .01 = .38.
To write a percent as a decimal:
For example, 75% = .75
Write a decimal as a percent
For example, .052 = 5.2%
Practice