+2446 I happen to remember what this decimal is represented in a fraction form, but here is the method one can use to convert 0.¯142857 into a fraction.
This first step is very simple; just set it equal to a variable. I'll use the normal x as my variable for this example. Therefore, 0.¯142857=x
The next goal is to get the repeating portion into the whole numbers part. It is probably easier showing by example than by explaining in words:
| 0.¯142857=x | Multiply by 1000000 on both sides. |
| 142857.¯142857=10000000x | As you can see, the repeating section is now in whole numbers. Now, subtract both equations from each other. |
| 142857=999999x | Now, divide by 999999 on both sides. |
| x=142857999999÷142857142857 | It is probably hard to realize here, but the GCF of the numerator and denominator is 142857. |
| x=17 | |
Look at that! 0.¯142857=17. That's quite a nice fraction.
