# Fractions, Decimals, and Percents

Remember that when you are dealing with decimals, the first place to the right of the decimal is the tenths place, the second place is the hundredths place, and the third place is the thousandths place, and so on.  Most statistics are reported to at least the hundredths place.  If there is no whole number before the decimal, it is customary to report a zero before the decimal.  This calls attention to the fact that you are dealing with a number smaller than one.

Many formulas in statistics contain fractions.  To understand what these formulas are doing, it is very helpful to recall the basics of fractions.  Fractions can be expressed two primary ways: With a horizontal line dividing the numerator (the top of a fraction) and denominator (the bottom of a fraction), or a slash dividing the numerator and denominator.

We can also divide the numerator by the denominator and get a proportion, which is a fraction expressed in decimal form.  We can easily convert that proportion to a percentage by multiplying it by 100 (which moves the decimal two places to the right).

```Examples:

2/3 =  = 0.6667 = 66.67%

1/2 =  = 0.5000 = 50.00%```

Remember the following characteristics of fractions:

• As the numerator increases, the value of the faction increases.
• As the denominator increases, the value of the fraction decreases.
• With complex fractions, perform all math operations in both the numerator and the denominator before dividing.

A percentage is a special fraction where the denominator is always 100, regardless of how many subjects we are describing.  If we say 50% of our subjects have a particular characteristic, we are saying that 50 out of 100 have it.  It may be helpful to recall that cent comes from Latin and means 100.  By using a common denominator, percentages are very useful in allowing us to compare groups of different sizes.  It also aids us in understanding the characteristics of large groups that we can’t intuitively grasp.

`To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100.`

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