Fractions Decimals and Percents Worksheets - Math Monks - Free Printable

Sure! Let’s solve each problem step by step and explain the reasoning.

---

## ① Convert each fraction into decimal.

To convert a fraction to a decimal, divide the numerator by the denominator.

a. $\frac{46}{100} = 46 \div 100 = \boxed{0.46}$
→ Since denominator is 100, move decimal point in numerator 2 places left.

b. $\frac{6}{100} = 6 \div 100 = \boxed{0.06}$

c. $\frac{292}{1000} = 292 \div 1000 = \boxed{0.292}$
→ Denominator is 1000 → move decimal 3 places left.

d. $\frac{46}{100} = \boxed{0.46}$ (same as part a)

---

## ② Convert each decimal into fraction.

Write the decimal as a fraction with denominator as power of 10, then simplify if possible.

a. $0.07 = \frac{7}{100}$ → already simplified → $\boxed{\frac{7}{100}}$

b. $0.67 = \frac{67}{100}$ → 67 is prime, so no simplification → $\boxed{\frac{67}{100}}$

c. $9.37 = 9 + 0.37 = 9 + \frac{37}{100} = \boxed{\frac{937}{100}}$ or mixed number $9\frac{37}{100}$

d. $27.17 = 27 + 0.17 = 27 + \frac{17}{100} = \boxed{\frac{2717}{100}}$ or $27\frac{17}{100}$

---

## ③ Convert each fraction into percent.

Multiply the fraction by 100% (or divide numerator by denominator, then multiply by 100).

a. $\frac{2}{7} \approx 0.2857 \times 100\% = \boxed{28.57\%}$ (rounded to two decimals)

b. $\frac{11}{12} \approx 0.9167 \times 100\% = \boxed{91.67\%}$

c. $\frac{100}{113} \approx 0.88495 \times 100\% = \boxed{88.50\%}$ (rounded to two decimals)

d. $\frac{20}{27} \approx 0.7407 \times 100\% = \boxed{74.07\%}$

---

## ④ Convert each percent into fraction.

Divide the percent by 100, then simplify.

a. $37.17\% = \frac{37.17}{100} = \frac{3717}{10000}$ → check for simplification: GCF of 3717 and 10000 is 1 → $\boxed{\frac{3717}{10000}}$

b. $805.11\% = \frac{805.11}{100} = \frac{80511}{10000}$ → simplify? GCF(80511,10000)=1 → $\boxed{\frac{80511}{10000}}$ or mixed number $8\frac{511}{10000}$

c. $6394.37\% = \frac{6394.37}{100} = \frac{639437}{10000}$ → GCF=1 → $\boxed{\frac{639437}{10000}}$

d. $0.09\% = \frac{0.09}{100} = \frac{9}{10000}$ → $\boxed{\frac{9}{10000}}$

---

## ⑤ Convert each percent into decimal.

Divide percent by 100 (move decimal point 2 places left).

a. $11.33\% = 11.33 \div 100 = \boxed{0.1133}$

b. $77\frac{1}{3}\% = 77.333...\% = 77.\overline{3}\% = \frac{232}{3}\% = \frac{232}{3} \div 100 = \frac{232}{300} = \frac{58}{75} \approx \boxed{0.7733}$ (repeating)

Alternatively: $77\frac{1}{3} \div 100 = \frac{232}{3} \times \frac{1}{100} = \frac{232}{300} = \boxed{0.77\overline{3}}$

c. $90\frac{1}{2}\% = 90.5\% = 90.5 \div 100 = \boxed{0.905}$

d. $80.3\% = 80.3 \div 100 = \boxed{0.803}$

---

## ⑥ Convert each decimal into percent.

Multiply decimal by 100% (move decimal point 2 places right).

a. $0.37 \times 100\% = \boxed{37\%}$

b. $0.22 \times 100\% = \boxed{22\%}$

c. $0.99 \times 100\% = \boxed{99\%}$

d. $0.01 \times 100\% = \boxed{1\%}$

---

✔ Final Answers Summary:

①

a. 0.46
b. 0.06
c. 0.292
d. 0.46

②

a. $\frac{7}{100}$
b. $\frac{67}{100}$
c. $\frac{937}{100}$ or $9\frac{37}{100}$
d. $\frac{2717}{100}$ or $27\frac{17}{100}$

③

a. 28.57%
b. 91.67%
c. 88.50%
d. 74.07%

④

a. $\frac{3717}{10000}$
b. $\frac{80511}{10000}$
c. $\frac{639437}{10000}$
d. $\frac{9}{10000}$

⑤

a. 0.1133
b. 0.7733... or $0.77\overline{3}$
c. 0.905
d. 0.803

⑥

a. 37%
b. 22%
c. 99%
d. 1%

Let me know if you’d like any step explained further!