Question

Перетворити дріб 2 /9 у нескінченний десятковий періодичній дріб.

Answer 1

2/9=0.222222222222222222222222..

Answer 2

I can help you with your math question. To convert a fraction to an infinite decimal periodic fraction, you need to divide the numerator by the denominator using long division. For example, to convert 2/9 to a decimal fraction, you need to do the following:

$$ \begin{array}{r} 0,\overline{2} \\ 9 \overline{)2,0000} \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}20 \\ \phantom{9}\underline{-18} \\ \phantom{9}\vdots \end{array} $$

As you can see, the remainder of 2 repeats indefinitely, so the decimal fraction is 0.222... with a period of 2. You can write this as $0,\overline{2}$ or $0.(2)$. You can also use online calculators to convert fractions to decimal fractions, such as [this one](https://www.rapidtables.org/uk/convert/number/Fraction_to_Decimal.html) or [this one](https://ua.onlinemschool.com/math/assistance/fraction/transform2/). You can also read more about infinite periodic decimal fractions and how to convert them to ordinary fractions [here](https://bankchart.com.ua/education/mathematics/arithmetic/neskinchenni_periodichni_desyatkovi_drobi_peretvorennya_u_zvichayni_drobiyu_urok_12) or [here](https://naurok.com.ua/peretvorennya-zvichaynih-drobiv-v-desyatkovi-desyatkovi-nablizhennya-zvichaynogo-drobu-259852.html). I hope this helps.