1. Let's start by understanding the three topics: fractions, percentages, and standard form. 2. Fractions represent parts of a whole and are written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator. 3. Percentages represent parts per hundred and are written as a number followed by \%. 4. Standard form (scientific notation) expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer. 5. To convert a fraction to a percentage, multiply by 100: $$\text{Percentage} = \frac{a}{b} \times 100\%$$ 6. To convert a percentage to a fraction, divide by 100 and simplify: $$\text{Fraction} = \frac{\text{Percentage}}{100}$$ 7. To convert a number to standard form, move the decimal point to create a number between 1 and 10, then multiply by $10^n$ where $n$ is the number of places moved. 8. Example: Convert $\frac{3}{4}$ to a percentage. 9. Multiply $\frac{3}{4} \times 100 = \frac{3 \times 100}{4} = \frac{300}{4}$. 10. Simplify by canceling common factors: $$\frac{\cancel{300}}{\cancel{4}} = 75\%$$ 11. Example: Convert 45\% to a fraction. 12. Write as $\frac{45}{100}$. 13. Simplify by dividing numerator and denominator by 5: $$\frac{\cancel{45}^9}{\cancel{100}^{20}} = \frac{9}{20}$$ 14. Example: Convert 0.0062 to standard form. 15. Move decimal 3 places right: $0.0062 = 6.2 \times 10^{-3}$. 16. Summary: Use these conversions to switch between fractions, percentages, and standard form easily. Final answers: - $\frac{3}{4} = 75\%$ - $45\% = \frac{9}{20}$ - $0.0062 = 6.2 \times 10^{-3}$