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 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)?
10x = 9.99999
- x = 0.999999
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=9 for x by dividing both sides of it by 9, we'll get that x=9/9. And this is your answer.
How is this your answer? Well remember that above, x was originally set equal to 0.999999 via x=0.999999, and now we have that x is also equal to 9/9, so that means 0.999999=9/9..and there's 0.999999 written as a fraction!
can be reduced further to 1, because anything over itself(other than zero) is 1.
The fraction 1 is not reduced to lowest 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)
or Greatest Common Factor (GCF) of the numbers 0 and 9.
So, this fraction reduced to lowest terms is 1
So your final answer is: 0.999999 can be written as the fraction 1