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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