Question
Write in decimal form and state what kind of decimal expansion: $\frac{3}{{13}}$
✓
Answer
$\frac{3}{{13}}$ On dividing $3$ by $13$, we get
We can observe that while dividing $3$ by $13$ we got the remainder as $3$, which will continue to be $3$ after carrying out $6$ continuous divisions.
Therefore, we conclude that $\frac{3}{{13}} = 0.230769.....{\text{ or }}\frac{3}{{13}} = 0.\overline {230769} $, which is a non-terminating decimal and recurring decimal.
We can observe that while dividing $3$ by $13$ we got the remainder as $3$, which will continue to be $3$ after carrying out $6$ continuous divisions.
Therefore, we conclude that $\frac{3}{{13}} = 0.230769.....{\text{ or }}\frac{3}{{13}} = 0.\overline {230769} $, which is a non-terminating decimal and recurring decimal.
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