Respuesta :
Answer:
2.318... = [tex]2\frac{106}{333}[/tex]
Step-by-step explanation:
The given number is 2.318 repeating.
So, let's take x = 2.318318...
318 repeating after the decimal point.
So multiply x with 1000
1000x = 1000*2.318318....
1000x = 2318.318...
This can be written as
1000x = 2316 + 2.318...
We know that x = 2.318....
1000x = 2316 + x
1000x - x = 2316
999x = 2316
Dividing both sides by 999, we get
x = [tex]\frac{2316}{999}[/tex]
x = [tex]2\frac{318}{999}[/tex]
Now we can simplify the fraction form by 3, we get
x = [tex]2\frac{106}{333}[/tex]
