Sumali sa komunidad ng IDNStudy.com at simulang makuha ang mga sagot. Makakuha ng mabilis at eksaktong sagot sa iyong mga tanong mula sa aming mga eksperto na laging handang tumulong.
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]
_____________________________
**** 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
_______________________________
I Hope this helps, greetings ... Dexteright02! =)