Question
Write in decimal form and say what kind of decimal expansion: $\frac{2}{{11}}$
✓
Answer
$\frac{2}{{11}}$ On dividing $2$ by $11$, we get
We can observe that while dividing $2$ by $11$, first we got the remainder as $2$ and then $9$, which will continue to be $2$ and $9$ alternately.
Therefore, we conclude that $\frac{2}{{11}} = 0.1818.....{\text{ or }}\frac{2}{{11}} = 0.\overline {18}$ , which is a non-terminating decimal and recurring decimal.
We can observe that while dividing $2$ by $11$, first we got the remainder as $2$ and then $9$, which will continue to be $2$ and $9$ alternately.
Therefore, we conclude that $\frac{2}{{11}} = 0.1818.....{\text{ or }}\frac{2}{{11}} = 0.\overline {18}$ , which is a non-terminating decimal and recurring decimal.
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