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change the repeating, non terminating decimals to fractions: 0.222....

Sagot :

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! =)