how is 0.3 repeating 1/3

3 tenths is written as 3/10

Also 0.6 repeating is apparently 2/3 but how?

6/10=3/5?

Question

how is 0.3 repeating 1/3 

3 tenths is written as 3/10 

Also 0.6 repeating is apparently 2/3 but how? 

6/10=3/5?

zepdrix · Answer

Let's call the number 0.3 repeating like... x or something,
$\large\rm x=0.333...$

If we multiply both sides of this assignment by 10,
$\large\rm 10x=3.333...$
The multiplication just moves the decimal one place, ya?

Then let's apply subtraction,$$\large\rm 10x-x=3.333...-0.333...$$On the left side of our equation, we have 9x,
on the right side, they have the same decimal portion, so those will subtract off,$$\large\rm 9x=3$$

zepdrix · Answer

Then divide to get the value for x,$$\large\rm x=\frac39$$

zepdrix · Answer

Which simplifies to 1/3.
Kind of a neat little trick, ya? :)

australia10 · Answer

Where are you getting the other x from?

australia10 · Answer

Thanks for helping just not sure how you worked it out.

otherworldly · Answer

do u want to know how 6/10 = 3/5