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Hello!
Change the repeating, non terminating decimals to fractions: 0.222....
Solving:
[Converting Repeating or Terminating Decimals to Fractions]
Periodic decimals are rational numbers with periodic decimals, and the repetition of these numbers forms the periodic part.
0.222 ... is the same as [tex]0.\overline{2}[/tex]
Let x = 0.222 ... and multiply both members by 10:
10x = 2.222 ...
By subtracting member to member, the first equality of the second:
→ 10x - x = 2.222 - 0.222
→ 9x = 2
→ x = 2/9
Thus the generatrix of [tex]0.222...[/tex] or [tex]0.\overline{2}[/tex]
Answer:
[tex]\boxed{\boxed{x = \dfrac{2}{9}}}\end{array}}\qquad\checkmark[/tex]
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**** Another way to solve:
[Converting Repeating or Terminating Decimals to Fractions]
0.222 ... has a period equal to 2
To form the fraction, use the numerator (as period) and the denominator (as digit 9, repeating the digit 9 according to the period quantity).
So:
0.222 ... = 2/9 <--- irreducible fraction
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I Hope this helps, greetings ... Dexteright02! =)