0.33333333333333333333333333333333333333333333333 simplified at a fraction

Accepted Solution

Answer:[tex]\frac{1}{3}[/tex]Step-by-step explanation:Your original number to convert is 0.333333. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 3).If we do this, we'll get a 3.333333 (slide the decimal in the 0.333333 right 1 places, you'll get 3.333333).So what? Well now, we have two numbers with the same repeating decimal parts, 3.333333 and 0.333333.Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x = 0.333333. The number with the decimal point slid over can be called 10x, because 10x = 3.33333310x = 3.33333-x = 0.333333[tex]\frac{10x = 3.33333  -x = 0.333333}{9x = 3}[/tex]---------------------------------------------------------------------------------------------Now, solving 9x=3 for x by dividing both sides of it by 9, we'll get that x=3/9. And this is your answer.How is this your answer? Well remember that above, x was originally set equal to 0.333333 via x = 0.333333, and now we have that x is also equal to 3/9, so that means 0.333333 = 3/9..and there's 0.333333 written as a fraction.-------------------------------------------------------------------------------------------Simplify 3/9 into the lowest terms:[tex]\frac{1}{3}[/tex]