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# Number Theory

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Convert 0.031\overline{4}\$ to a fraction in simplest form.

Jun 18, 2024

#1
+1252
+1

We can solve this problem by defining variables and using a nice little trick.

First, let's set $$x = 0.031\overline{4}$$. we are trying to put x in fractional form.

For that value of x, we have that $$10 x = 0.314\overline{4}$$

Now, we subtract x from 10x. We get

$$10x-x = 0.314\overline{4}-0.031\overline{4}$$

Since the repeating 4 cancels out, we are left with

$$9 x = 0.283$$

Now, we simplfy solve for x.

$$x = \frac{0.283}{9}$$

$$x=\frac{0.283}{9}\times \frac{1000}{1000}= \frac{283}{9000}$$

So, we have

$$0.031\overline{4} = \frac{283}{9000}$$

So 283/9000 is our final answer.

Thanks! :)

Jun 18, 2024

#1
+1252
+1

We can solve this problem by defining variables and using a nice little trick.

First, let's set $$x = 0.031\overline{4}$$. we are trying to put x in fractional form.

For that value of x, we have that $$10 x = 0.314\overline{4}$$

Now, we subtract x from 10x. We get

$$10x-x = 0.314\overline{4}-0.031\overline{4}$$

Since the repeating 4 cancels out, we are left with

$$9 x = 0.283$$

Now, we simplfy solve for x.

$$x = \frac{0.283}{9}$$

$$x=\frac{0.283}{9}\times \frac{1000}{1000}= \frac{283}{9000}$$

So, we have

$$0.031\overline{4} = \frac{283}{9000}$$

So 283/9000 is our final answer.

Thanks! :)

NotThatSmart Jun 18, 2024