Question

Write .112112 as a fraction

Answer 1

Answer:

112/999

Explanation:

Here's how to convert 0.112112 to a fraction...

The decimal part of your number seems to have the digits 112 repeating in it.

Your original number to convert is 0.112112. Let's slide the decimal point in this number to the right 3 place(s) (the same number of digits in the number 112).

If we do this, we'll get a 112.112000 (slide the decimal in the 0.112112 right 3 places, you'll get 112.112000).

So what? Well now, we have two numbers with the same repeating decimal parts, 112.112000 and 0.112112.

Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x=0.112112. The number with the decimal point slid over can be called 1000x, because 1000x=112.112000

What if we subtracted these two equations (that is, subtract the items on the left of the equal sign

from the stuff on the right of the equal sign)?

1000x = 112.112

- x = 0.112112

---------------

999x = 112.

Now here's the important result of doing all of this: Notice how all of the repeating decimal parts have subtracted away to zero! We are left with a nice, simple 112 on the right side of the equal sign.

Now, solving 999x=112 for x by dividing both sides of it by 999, we'll get that x=112/999. And this is your answer.

How is this your answer? Well remember that above, x was originally set equal to 0.112112 via x=0.112112, and now we have that x is also equal to 112/999, so that means 0.112112=112/999..and there's 0.112112 written as a fraction!

So your final answer is: 0.112112 can be written as the fraction 112/999