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In $13-22,$ write each decimal as a common fraction.$$0.5 \overline{7}$$

$\frac{26}{45}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 1

Rational Numbers

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

Campbell University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

00:30

In $13-22,$ write each dec…

01:17

01:05

01:20

02:19

00:25

01:57

01:23

01:45

Write each fraction as a d…

Okay, so we're gonna take the desk. Well, the repeating decimal, where the seven repeats here of 0.57 and turn it into a fraction until what we do is we set X equal to this decimal here, and I want to encompass the repeating decimal here. And so what I've got is all multiply times 100 and that will get my decimal over, too after the repeating seven. So now everything after this decimal repeats and I'm going to subtract a 10 X because this part here doesn't repeat. So I have to have the second number that I'm subtracting here has to have everything repeating from the right of the decimal on. And that's why we have to start with 100 acts and then subtract a 10 X because now I have this 5.77 and see how all of these from the right side of the decimal after when I subtract will disappear. Right? Because seven minus seven is equal to zero. And this continues on and on forever. And so this will become a zero. Here I get a two and a five when I subtract 10 from 100 I get a 90 X, I divide both sides by 90 and I get that X is equal to 52 over 90. But we see both of these are even so. They're both divisible, um, by two. And so when I get divide both by two, I get a 26 and the numerator and I get 45 in the denominator. And any time you do these, all you want to do is do a quick check on your calculator. When you divide 26 by 45 you should get this answer, and you do indeed, get this answer. So we've done this correctly.

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