The decimal part of your number seems to have the repeating digit 9 in it.

Your original number to convert is 0.999999. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 9).If we do this, we'll get a 9.999990 (slide the decimal in the 0.999999 right 1 places, you'll get 9.999990).

So what? Well now, we have two numbers with the same repeating decimal parts, 9.999990 and 0.999999.

Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x=0.999999. The number with the decimal point slid over can be called 10x, because 10x=9.999990

What if we

subtractedthese two equations (that is, subtract the items on the left of the equal sign

from the stuff on the right of the equal sign)?10x = 9.99999

- x = 0.999999

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9x = 8.99999.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 9 on the right side of the equal sign.

Now, solving

9x=9forxby dividing both sides of it by 9, we'll get thatx=9/9. And this is your answer.How is this your answer? Well remember that above,

xwas originally set equal to 0.999999 viax=0.999999, and now we have thatxis also equal to 9/9, so that means 0.999999=9/9..and there's 0.999999 written as a fraction!

This fraction,

can be reduced further to1, because anything over itself(other than zero) is 1.

The fraction1is not reduced tolowest terms. We can reduce this fraction to lowest

terms by dividing both the numerator and denominator by 9.

Why divide by 9? 9 is the

Greatest Common Divisor (GCD)

orGreatest Common Factor (GCF)of the numbers 0 and 9.

So, this fraction reduced to lowest terms is1

So your final answer is: 0.999999 can be written as the fraction

1