1. **Fill in the blanks in the table:** Percent | Fraction | Decimal ---|---|--- 50% | 1/2 | 0.5 10% | 1/10 | 0.1 90% | \frac{9}{10} | 0.9 25% | 1/4 | 0.25 160% | \frac{16}{10} | 1.60 87.5% | \frac{7}{8} | 0.875 120% | \frac{12}{10} | 1.20 **Explanation:** - Percent means per hundred, so 90% = 90/100 = \frac{9}{10} and decimal is 0.9. - For 87.5%, it is 87.5/100 = 0.875 and fraction is \frac{7}{8}. 2. **Convert and solve in scientific notation:** **a.** 7381.79 Step 1: Write 7381.79 as a number between 1 and 10 times a power of 10. $$7381.79 = 7.38179 \times 10^3$$ **b.** 0.09 Step 1: Write 0.09 as a number between 1 and 10 times a power of 10. $$0.09 = 9 \times 10^{-2}$$ **c.** $ (7 \times 10^2) \times (150 \times 10^4) $ Step 1: Multiply the coefficients and add exponents of 10. $$7 \times 150 = 1050$$ $$10^2 \times 10^4 = 10^{2+4} = 10^6$$ Step 2: Combine: $$1050 \times 10^6$$ Step 3: Convert 1050 to scientific notation: $$1050 = 1.05 \times 10^3$$ Step 4: So, $$1.05 \times 10^3 \times 10^6 = 1.05 \times 10^{9}$$ **d.** $ (0.03 \times 10^5) \times (1.3 \times 10^{-2}) $ Step 1: Multiply coefficients: $$0.03 \times 1.3 = 0.039$$ Step 2: Add exponents: $$10^5 \times 10^{-2} = 10^{5-2} = 10^3$$ Step 3: Combine: $$0.039 \times 10^3$$ Step 4: Convert 0.039 to scientific notation: $$0.039 = 3.9 \times 10^{-2}$$ Step 5: So, $$3.9 \times 10^{-2} \times 10^3 = 3.9 \times 10^{1}$$ **e.** $ \frac{600 \times 10^{-3}}{20 \times 10^{2}} $ Step 1: Divide coefficients: $$\frac{600}{20} = 30$$ Step 2: Subtract exponents: $$10^{-3} \div 10^{2} = 10^{-3-2} = 10^{-5}$$ Step 3: Combine: $$30 \times 10^{-5}$$ Step 4: Convert 30 to scientific notation: $$30 = 3.0 \times 10^{1}$$ Step 5: So, $$3.0 \times 10^{1} \times 10^{-5} = 3.0 \times 10^{-4}$$ **f.** $ (2 \times 10^{-2}) + (3 \times 10^{-3}) $ Step 1: Convert both to the same power of 10 for addition. $$2 \times 10^{-2} = 20 \times 10^{-3}$$ Step 2: Add coefficients: $$20 + 3 = 23$$ Step 3: So, $$23 \times 10^{-3}$$ Step 4: Convert 23 to scientific notation: $$23 = 2.3 \times 10^{1}$$ Step 5: So, $$2.3 \times 10^{1} \times 10^{-3} = 2.3 \times 10^{-2}$$ **Final answers:** a. $7.38179 \times 10^3$ b. $9 \times 10^{-2}$ c. $1.05 \times 10^{9}$ d. $3.9 \times 10^{1}$ e. $3.0 \times 10^{-4}$ f. $2.3 \times 10^{-2}$