* 10. a. Write 0.080 as a fraction. b. Write $$ 37 \frac{1}{2} \% $$ as a decimal. c. Write $$ \frac{1}{11} $$ as a decimal with a bar over the repetend.

Question

UpStudy AI · Accepted Answer

**a. Write $$0.080$$ as a fraction:**

1. Express $$0.080$$ as $$\frac{80}{1000}$$.
2. Simplify the fraction by dividing the numerator and denominator by 10: $$\frac{80 \div 10}{1000 \div 10} = \frac{8}{100}$$.
3. Further simplify by dividing numerator and denominator by 2: $$\frac{8 \div 2}{100 \div 2} = \frac{4}{50}$$.
4. Finally, divide numerator and denominator by 2 again: $$\frac{4 \div 2}{50 \div 2} = \frac{2}{25}$$.

Thus, $$0.080 = \frac{2}{25}$$.

---

**b. Write $$37 \frac{1}{2}\%$$ as a decimal:**

1. Convert the mixed number to an improper fraction:
   $$
   37 \frac{1}{2} = \frac{(37 \times 2) + 1}{2} = \frac{74 + 1}{2} = \frac{75}{2}
   $$
2. Rewrite the percentage as a decimal by dividing by $$100$$:
   $$
   \frac{75}{2}\% = \frac{75}{2} \times \frac{1}{100} = \frac{75}{200}
   $$
3. Simplify the fraction by dividing numerator and denominator by $$25$$:
   $$
   \frac{75 \div 25}{200 \div 25} = \frac{3}{8}
   $$
4. Convert $$\frac{3}{8}$$ to a decimal:
   $$
   \frac{3}{8} = 0.375
   $$

Thus, $$37 \frac{1}{2}\% = 0.375$$.

---

**c. Write $$\frac{1}{11}$$ as a decimal with a bar over the repetend:**

1. Divide $$1$$ by $$11$$:
   $$
   \frac{1}{11} = 0.090909\ldots
   $$
2. Since the digits $$09$$ repeat indefinitely, we express the decimal as:
   $$
   0.\overline{09}
   $$

Thus, $$\frac{1}{11} = 0.\overline{09}$$.
a. $$0.080 = \frac{2}{25}$$ b. $$37 \frac{1}{2}\% = 0.375$$ c. $$\frac{1}{11} = 0.\overline{09}$$

* 10. a. Write 0.080 as a fraction. b. Write \( 37 \frac{1}{2} \% \) as a decimal. c. Write \( \frac{1}{11} \) as a decimal with a bar over the repetend.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Arithmetic Questions