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2 Out of 22 As a Percentage

# 2 Out of 22 As a Percentage

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One out of twelve women use the internet. Half of them have never been online.

### Percentage

Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at \$200 and the price rises 10% (an increase of \$20), the new price will be \$220. Note that this final price is 110% of the initial price (100% + 10% = 110%).

In the case of interest rates, a very common but ambiguous way to say that an interest rate rose from 10% per annum to 15% per annum, for example, is to say that the interest rate increased by 5%, which could theoretically mean that it increased from 10% per annum to 10.05% per annum. It is clearer to say that the interest rate increased by 5 percentage points (pp). The same confusion between the different concepts of percent(age) and percentage points can potentially cause a major misunderstanding when journalists report about election results, for example, expressing both new results and differences with earlier results as percentages. For example, if a party obtains 41% of the vote and this is said to be a 2.5% increase, does that mean the earlier result was 40% (since 41 = 40 × (1

When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form. (Source: visualfractions.com)

### Value

Another common mistake is interpreting differences in percentages. Sometimes, readers jump to conclusions without looking at the percentages up close. We’re tempted to think that a greater value indicates a greater percentage growth. But that’s not always the case. For instance, suppose that the price of a video game went up from \$15 to \$30 one year. The following year, it increased to \$50.

Each of these comparisons derive the percentage in different ways. When measuring changes in size, you compare the difference between the new value and the old one. In our first example, let’s assume that the investor’s starting principal is \$2,000. If the growth is 4%, here’s how much they made over the year. (Source: www.calculators.org)

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