Question

classify the following as a repeating or a terminating decimal (and write what that decimal is). circle one below
9 (4\frac{3}{5}=)
terminating repeating
10 (\frac{1}{4}=)
terminating repeating

1. (\frac{4}{33}=)

terminating repeating

1. (4\frac{7}{20}=)

terminating repeating

1. (\frac{7}{11}=)

terminating repeating

1. (\frac{9}{50}=)

terminating repeating
15 (\frac{2}{111}=)
terminating repeating

1. (\frac{4}{125}=)

terminating repeating

1. (\frac{5}{33}=)

terminating repeating

1. (3\frac{1}{3}=)

terminating repeating

1. (2\frac{2}{25}=)

terminating repeating

1. (\frac{2}{5}=)

terminating repeating

Explanation:

Step1: Convert mixed - number to improper fraction

For $4\frac{3}{5}=\frac{4\times5 + 3}{5}=\frac{23}{5}=4.6$, terminating.

Step2: Simplify fraction

$\frac{1}{4}=0.25$, terminating.

Step3: Divide numerator by denominator

$\frac{4}{33}=0.\overline{12}$, repeating.

Step4: Convert mixed - number to improper fraction

$4\frac{7}{20}=\frac{4\times20+7}{20}=\frac{87}{20}=4.35$, terminating.

Step5: Divide numerator by denominator

$\frac{7}{11}=0.\overline{63}$, repeating.

Step6: Simplify fraction

$\frac{9}{50}=0.18$, terminating.

Step7: Divide numerator by denominator

$\frac{2}{111}=0.\overline{018}$, repeating.

Step8: Simplify fraction

$\frac{4}{125}=0.032$, terminating.

Step9: Divide numerator by denominator

$\frac{5}{33}=0.\overline{15}$, repeating.

Step10: Convert mixed - number to improper fraction

$3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3}=3.\overline{3}$, repeating.

Step11: Convert mixed - number to improper fraction

$2\frac{2}{25}=\frac{2\times25+2}{25}=\frac{52}{25}=2.08$, terminating.

Step12: Simplify fraction

$\frac{2}{5}=0.4$, terminating.

Answer:

1. 4.6, Terminating
2. 0.25, Terminating
3. $0.\overline{12}$, Repeating
4. 4.35, Terminating
5. $0.\overline{63}$, Repeating
6. 0.18, Terminating
7. $0.\overline{018}$, Repeating
8. 0.032, Terminating
9. $0.\overline{15}$, Repeating
10. $3.\overline{3}$, Repeating
11. 2.08, Terminating
12. 0.4, Terminating