Representing Rational NumbersDate: 09/17/2002 at 19:38:34 From: Kellsey Subject: Percents, fractions, decimals What do fractions, decimals, and percents have in common? Date: 09/18/2002 at 10:15:20 From: Doctor Ian Subject: Re: Percents, fractions, decimals Hi Kellsey, They're all just different ways of representing rational numbers. For example, let's look at the decimal number 0.125. What this _means_ is 0.125 = 0 + 1/10 + 2/100 + 5/1000 That is, each decimal place corresponds to a different fraction, and the number itself is the sum of these fractions. Now, suppose we adjust this so that all the fractions have a denominator of 100: 0.125 = 0 + 10/100 + 2/100 + 0.5/100 Now we can use the distributive property to add them together: 0.125 = 0 + (10 + 2 + 0.5)/100 = 12.5/100 A fraction whose denominator is 100 is given the special name of 'percent' (which literally means 'for each hundred'). So 0.125 = 12.5% But can we make this fraction simpler? In fact, we can: 12.5/100 = 25/200 = 1/8 So 0.125 = 12.5% = 1/8 Now, all of these mean exactly the same thing, but they're different ways of writing it. Which form you use depends on what you're trying to do. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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