Answer:1 1/4
Step-by-step explanation:
Here's how to convert 0.555555555 to a fraction...
The decimal part of your number seems to have the repeating digit 5 in it.
Your original number to convert is 0.555556. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 5).
If we do this, we'll get a 5.555556 (slide the decimal in the 0.555556 right 1 places, you'll get 5.555556).
So what? Well now, we have two numbers with the same repeating decimal parts, 5.555556 and 0.555556.
Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x=0.555556. The number with the decimal point slid over can be called 10x, because 10x=5.555556
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)?Here's how to convert 0.555555555 to a fraction...
The decimal part of your number seems to have the repeating digit 5 in it.
Your original number to convert is 0.555556. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 5).
If we do this, we'll get a 5.555556 (slide the decimal in the 0.555556 right 1 places, you'll get 5.555556).
So what? Well now, we have two numbers with the same repeating decimal parts, 5.555556 and 0.555556.
Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x=0.555556. The number with the decimal point slid over can be called 10x, because 10x=5.555556
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)?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 5 on the right side of the equal sign.
Now, solving 9x=5 for x by dividing both sides of it by 9, we'll get that x=5/9. And this is your answer.
How is this your answer? Well remember that above, x was originally set equal to 0.555556 via x=0.555556, and now we have that x is also equal to 5/9, so that means 0.555556=5/9..and there's 0.555556 written as a fraction!
So your final answer is: 0.555556 can be written as the fraction
