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# Decimals

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2
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+764

Express 2.\overline{57} as a base 10 fraction in reduced form.

Jun 14, 2024

#1
+1252
+1

We can use variables and equations to solve this problem.

First, let's let $$x=2.\overline{57}$$

If we have that for the value of x, we have $$100x = 257.\overline{57}$$

This is extremely important for our solution.

Now, we subtract x from 100x. We have

$$100x-x=257.\overline{57}-2.\overline{57}$$

Notice the repeating decimal cancels out. We get

$$99x=255\\ x=255/99\\ x=\frac{85}{33}\\ x=2\frac{19}{33}\\$$

So our final answer is $$x=2\frac{19}{33}$$

Thanks! :)

Jun 14, 2024

#1
+1252
+1

We can use variables and equations to solve this problem.

First, let's let $$x=2.\overline{57}$$

If we have that for the value of x, we have $$100x = 257.\overline{57}$$

This is extremely important for our solution.

Now, we subtract x from 100x. We have

$$100x-x=257.\overline{57}-2.\overline{57}$$

Notice the repeating decimal cancels out. We get

$$99x=255\\ x=255/99\\ x=\frac{85}{33}\\ x=2\frac{19}{33}\\$$

So our final answer is $$x=2\frac{19}{33}$$

Thanks! :)

NotThatSmart Jun 14, 2024