Write the following in decimal form and say what kind of decimal expansion each has : (i) 36/100 (ii) 1/11 (iii) 4 1/8 (iv) 3/13 (v) 2/11 (vi) 329/400

Write the following in decimal form and say what kind of decimal expansion each has :

(i) $\frac{36}{100}$

(ii) $\frac{1}{11}$

(iii) $4 \frac{1}{8}$

(iv) $\frac{3}{13}$

(v) $\frac{2}{11}$

(vi) $\frac{329}{400}$

Here are the decimal forms of the given fractions along with the types of decimal expansion each has:

(i) $\frac{36}{100}$ in decimal form is $0.36$. This is a terminating decimal because it comes to a definite end.

(ii) $\frac{1}{11}$ in decimal form is approximately $0.090909...$, which can be represented as $0.\overline{09}$. This is a repeating decimal with a repeating period of $09$.

(iii) $4 \frac{1}{8}$ in decimal form is $4.125$. This is another example of a terminating decimal.

(iv) $\frac{3}{13}$ in decimal form is approximately $0.230769...$, which can be represented as $0.\overline{230769}$. This is a repeating decimal with a repeating period of $230769$.

(v) $\frac{2}{11}$ in decimal form is approximately $0.181818...$, which can be represented as $0.\overline{18}$. This is a repeating decimal with a repeating period of $18$.

(vi) $\frac{329}{400}$ in decimal form is $0.8225$. This too is a terminating decimal.

So, among the given fractions, (i), (iii), and (vi) have terminating decimal expansions, while (ii), (iv), and (v) have repeating decimal expansions.