Why Does Division Convert a Fraction to a Decimal?
Date: 01/04/2009 at 20:18:24 From: Claudia Subject: Fractions to decimals Why do you divide the denominator into the numerator to get a decimal? What is the math behind this? It just seems odd that there is no explanation as to why this operation transfers a fraction to a base 10 decimal. I want to understand WHY this happens and the reasoning behind it. I am thinking that you are trying to get the denominator as close to 100 as possible so that you can make the fractions equivalent to decimals. I am just not sure why division gives the appropriate decimal to us.
Date: 01/04/2009 at 22:58:53 From: Doctor Peterson Subject: Re: Fractions to decimals Hi, Claudia. A fraction is essentially a division; in algebra we use the fraction bar as the standard division sign, and for good reason. Let's take a look. First, consider a fraction like 1/4. In pictures, you can think of that as a pie divided into 4 equal parts, and we just take one of them. Can you see how that is 1 divided by 4? Just as dividing 12 by 4 would mean dividing 12 objects into 4 equal parts (3 each) and taking one of them, dividing 1 by 4 means dividing 1 object (our pie) into 4 equal parts (now pieces, not wholes) and taking one of them. Now, how about when the numerator is not 1? Consider 3/4. We can think of this as starting with ONE pie, dividing it into 4 pieces, and taking 3 of them; but we can also think of starting with THREE pies, dividing EACH of them into 4 pieces (making 12 in all), and taking one from EACH pie. The 3 pieces we took are 1/4 of the 12 pieces; we've divided the 3 pies by 4 (and could, if we wished, give each of 4 people 3 quarters, so we've divided the 3 pies among 4 people). A more sophisticated way of looking at fractions is not to think in terms of pies, but multiplication and division of numbers. When we write "12 divided by 4 is 3", we mean that 3 is the number by which you have to multiply 4 to get 12. Similarly, what does it mean to talk about 3 divided by 4? It's the number by which you can multiply 4 to get 3. And 3/4 times 4 is 3, so that's the answer: 3 divided by 4 is 3/4. Now, when we convert a fraction to a decimal, all we are doing is carrying out, in decimal form, the division that the fraction represents. That is, in my example, we've said that 3/4 means 3 divided by 4, so we go ahead and divide 3.00 by 4 and get 0.75. Since both 3/4 and 0.75 are obtained by dividing 3 by 4, they are two ways to express the same number! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 01/04/2009 at 23:22:50 From: Claudia Subject: Thank you (Fractions to decimals) Thank you so much for your explanation. I have a better understanding now! I really appreciate it. Claudia
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