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Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. $$\frac{5}{11}$$
$\frac{5}{11}=0.45$
Algebra
Chapter 1
An Introduction to Algebra
Section 3
The Real Numbers
The Language of Algebra
Equations and Inequalities
Functions
Linear Functions
Quadratic Functions
Polynomials
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Let's divide out the Fraction 5/11 into decimal form. In order to do this, we put the numerator on the inside of the division symbol with a bunch of zeros after it. Just so we have room for the decibel. Now the outside we put the denominator. 11. Let's get started. So how many times can 11 go into five? Well, thats zero, but how many times can 11 go into 50? That's more like it. Well, 11 times four is 44 11 times five is 55. So we can say that it goes in four times before it goes over. So now we subtract 11 times four or 44 and we get six. All right, that's some progress. Now let's carry down a zero and we've got 60. So how many times can 11 going to 60? Well, 11 times five is 55 11 times six is 66 so it can only go in five times before it goes over. Now we can subtract 11 times five, which is 55 giving us 05 and we can carry another zero down to give us 50. So how does 11 go into 50. While we've already answered this question, it goes in four times so we could do the same thing that we did in the first step. Subtracting 44 getting a six carrying a zero down to get 60. How many times can 11 go to 60? Well, that's pretty familiar as well. It could go in five times once again. We also tracked out 55 and we'll be left with a five, which you can turn to a 50 by carrying down zero. Well, this looks like a repeating pattern. We've got 60 then 50 then 60 than 50 which once attracted on the top, gives 4545 and so on. This pattern is never going to be broken, so this is going to be a repeating decimal. Thus, we can write 5/11 in decimal form as 0.45 with a repeat bar over the 45 that is 0.45 repeating
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