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viktelen [127]
3 years ago
11

Write the following number as ratios of integers

Mathematics
1 answer:
Grace [21]3 years ago
5 0

We're going to "cut" the repeating part here in a few steps. First, we're going to put the number in a variable:

x=-2.0\overline{42}

Next, to get rid of the negative, we can multiply either side by -1 to get

-x=2.0\overline{42}

Now, we won't actually use this -x directly; instead, we want to create two new values, one by multiplying either side by 10:

-10x=20.\overline{42}

and the other by multiplying either side by 1000:

-1000x=2042.\overline{42}

Next, we can get rid of the repeated part of the number by subtracting -10x from -1000x:

-1000x-(-10x)=2042.\overline{42}-20.\overline{42}\\ -1000x+10x=2022\\ -990x=2022

And finally, we can divide either side of the equation by -990 to find that

x= \frac{2022}{-990}=-\frac{2022}{990}\div \frac{6}{6}=-\frac{337}{165}

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