Question

terminating and repeating decimals
write each fraction or mixed number as a decimal. use bar notation if needed.

1. $\frac{16}{20}$
2. $\frac{30}{120}$
3. $\frac{7}{18}$
4. $\frac{1}{6}$
5. $5\frac{11}{40}$
6. $5\frac{13}{50}$
7. $\frac{55}{300}$
8. $1\frac{1}{2}$
9. $\frac{5}{9}$
10. $2\frac{3}{4}$
11. $\frac{9}{11}$
12. $4\frac{1}{9}$

Explanation:

Step1: Convert $\frac{16}{20}$ to decimal

Divide 16 by 20: $16 \div 20 = 0.8$

Step2: Convert $\frac{30}{120}$ to decimal

Simplify first: $\frac{30}{120}=\frac{1}{4}$, then $1 \div 4 = 0.25$

Step3: Convert $1\frac{7}{8}$ to decimal

Convert the fraction: $7 \div 8 = 0.875$, then add the whole number: $1 + 0.875 = 1.875$

Step4: Convert $\frac{1}{6}$ to decimal

Divide 1 by 6: $1 \div 6 = 0.1\overline{6}$ (repeating decimal)

Step5: Convert $5\frac{11}{40}$ to decimal

Convert the fraction: $11 \div 40 = 0.275$, then add the whole number: $5 + 0.275 = 5.275$

Step6: Convert $5\frac{13}{50}$ to decimal

Convert the fraction: $13 \div 50 = 0.26$, then add the whole number: $5 + 0.26 = 5.26$

Step7: Convert $\frac{55}{300}$ to decimal

Simplify first: $\frac{55}{300}=\frac{11}{60}$, then $11 \div 60 = 0.18\overline{3}$ (repeating decimal)

Step8: Convert $1\frac{1}{2}$ to decimal

Convert the fraction: $1 \div 2 = 0.5$, then add the whole number: $1 + 0.5 = 1.5$

Step9: Convert $\frac{5}{9}$ to decimal

Divide 5 by 9: $5 \div 9 = 0.\overline{5}$ (repeating decimal)

Step10: Convert $2\frac{3}{4}$ to decimal

Convert the fraction: $3 \div 4 = 0.75$, then add the whole number: $2 + 0.75 = 2.75$

Step11: Convert $\frac{9}{11}$ to decimal

Divide 9 by 11: $9 \div 11 = 0.\overline{81}$ (repeating decimal)

Step12: Convert $4\frac{1}{9}$ to decimal

Convert the fraction: $1 \div 9 = 0.\overline{1}$, then add the whole number: $4 + 0.\overline{1} = 4.\overline{1}$

Answer:

s (for each problem):

1. $0.8$
2. $0.25$
3. $1.875$
4. $0.1\overline{6}$
5. $5.275$
6. $5.26$
7. $0.18\overline{3}$
8. $1.5$
9. $0.\overline{5}$
10. $2.75$
11. $0.\overline{81}$
12. $4.\overline{1}$