Write in decimal form and say what kind of decimal expansion it is. 3/13

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Solution

Dear Student,

$\frac{3}{13} = 0.2307692307692308 . . . = 0.230769$
The denominator of $\frac{3}{13}$ is 13 whose prime factorisation cannot be written in the form $2^{m} 5^{n}, w h e r e m, n \in W h o l e n u m b e r s$ .
Therefore, the decimal expansion is NON-TERMINATING AND REPEATING.

Regards,

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