Verified answer

34/204 is your fraction. You can simplify it if you want, but it's already a fraction. Both 34 and 204 have 34 as a factor, so this simplifies to 1/6.

If you wanted to start with 0.166666, then find the repeating bit. In this case it starts in the hundreds place and is a single digit (6).

So your decimal can be broken down into 0.1 + 0.0(6) repeating. Take the repeating part and put it over as many "9"s as there are digits in the repeating part. Here, that's just 1 digit.

6/9

Since it was in the hundredths place, multiply the denominator by 10.

6/90

1/10 + 6/90

9/90 + 6/90

15/90

1/6.

Hi! We know that the fraction 34/204 = 0.1666666666666666..., and now we want to convert this decimal back to a fraction. The procedure to do this relies on a little trick I'll show you below.

So, say we let the variable x = 0.16666666666.... Then, notice that I can write 100x = 16.66666666666...

Now, let's subtract these two values,

99x = 100x - x = 16.66666666666... - 0.16666666666... = 16.5

So, we have 99x = 16.5. If we divide by 99, we get x = 16.5 / 99 = 33 / 198 = 1/6 (198 / 33 = 6).

So, we can also write the decimal x = 0.16666666... as 1/6. This checks too, as our original fraction 34/204 also reduces to 1/6 (204/34 = 6).

Hope this helps, and please pick for best answer!

That fraction is actually 0.166666... (with 6's going on forever.

So if you call it n, we have:

n = 0.16666..

Multiply both sides by 100, you get:

100n = 16.6666...

Now you can subtract the first from the second, this cancels out the repeated 6's, so now you have an equation that you can solve:

99n = 16.6666... - 0.16666...

99n = 16.66 - 0.16

99n = 16.5

Now divide both sides by 99:

n = 16.5 / 99

Multiply both sides by 2 to get rid of the "half" decimal in the numerator:

n = 33/198

This reduces to: 1/6

So 34/204 = 0.16666... = 1/6

https://www.khanacademy.org/math/algebra/solving-l...