Question

repeating decimals
change $\frac{7}{22}$ to a decimal.

step 1: divide until the quotient ends or repeats.
step 2: put a decimal point in the quotient directly over the decimal point in the dividend.
step 3: write a bar over the part of the quotient that repeats.
$\frac{7}{22} = 0.3overline{18}$

change each fraction to decimal form.

1. $\frac{8}{11}$
2. $\frac{7}{12}$
3. $\frac{4}{9}$
4. $\frac{10}{22}$
5. $\frac{20}{24}$
6. $\frac{21}{36}$
7. $\frac{2}{45}$
8. $\frac{7}{30}$
9. $\frac{2}{18}$
10. $\frac{5}{27}$
11. $\frac{11}{33}$
12. $\frac{13}{45}$

Explanation:

Step1: Divide 8 by 11

$8 \div 11 = 0.\overline{72}$

Step2: Divide 7 by 12

$7 \div 12 = 0.58\overline{3}$

Step3: Divide 4 by 9

$4 \div 9 = 0.\overline{4}$

Step4: Simplify & divide 10/22

$\frac{10}{22}=\frac{5}{11}$, $5 \div 11 = 0.\overline{45}$

Step5: Simplify & divide 20/24

$\frac{20}{24}=\frac{5}{6}$, $5 \div 6 = 0.8\overline{3}$

Step6: Simplify & divide 21/36

$\frac{21}{36}=\frac{7}{12}$, $7 \div 12 = 0.58\overline{3}$

Step7: Divide 2 by 45

$2 \div 45 = 0.0\overline{4}$

Step8: Divide 7 by 30

$7 \div 30 = 0.2\overline{3}$

Step9: Simplify & divide 2/18

$\frac{2}{18}=\frac{1}{9}$, $1 \div 9 = 0.\overline{1}$

Step10: Divide 5 by 27

$5 \div 27 = 0.\overline{185}$

Step11: Simplify & divide 11/33

$\frac{11}{33}=\frac{1}{3}$, $1 \div 3 = 0.\overline{3}$

Step12: Divide 13 by 45

$13 \div 45 = 0.2\overline{8}$

Answer:

1. $0.\overline{72}$
2. $0.58\overline{3}$
3. $0.\overline{4}$
4. $0.\overline{45}$
5. $0.8\overline{3}$
6. $0.58\overline{3}$
7. $0.0\overline{4}$
8. $0.2\overline{3}$
9. $0.\overline{1}$
10. $0.\overline{185}$
11. $0.\overline{3}$
12. $0.2\overline{8}$