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In $13-22,$ write each decimal as a common fraction.$$0 . \overline{6}$$

$\frac{2}{3}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 1

Rational Numbers

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:23

In $13-22,$ write each dec…

01:05

00:30

01:57

01:53

01:20

00:25

02:19

01:25

express each repeating dec…

Okay, So what we want to do is switch this repeating decimals into a fraction. And the way that you do this is we're going to say we're gonna let X equal to this 0.6 that repeats. So when you only have it repeating in the 10th position if you multiply that by 10. 10 x So if I multiply this by ton, remember and move this one decimal place. So this and remember, this continues to repeat, Repeat, repeat. So this 10 Times X is equal to 6.66 And this keeps going on. And then if I subtract acts from both sides so here I would say remember that X was equal to this. So we'll put those equal there. And then when I subtract all of this stuff here, cancels out because we're subtracting and ex from this side and subtracting X from the side. And so when I subtract, I end up with six by itself. Here I'd get nine. X is equal to six to solve for X on Divide both sides by nine and you can see that this will reduce so I can divide top and bottom by three and I get 2/3. And if you use your calculator, you'll see that 2/3 indeed gives us this.

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