Subjects mathematics

Fractions Percentages 78D308

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1. **Stating the problem:** We will review how to work with fractions, percentages, and standard form (scientific notation). 2. **Fractions:** A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator. 3. **Percentages:** A percentage is a fraction out of 100. To convert a fraction to a percentage, multiply by 100 and add the % sign. 4. **Standard form:** Also called scientific notation, it expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer. 5. **Example:** Convert $\frac{3}{4}$ to a percentage and standard form. 6. Multiply $\frac{3}{4}$ by 100 to get the percentage: $$\frac{3}{4} \times 100 = \frac{3 \times 100}{4} = \frac{300}{4}$$ 7. Simplify the fraction: $$\frac{\cancel{300}}{\cancel{4}} = 75$$ 8. So, $\frac{3}{4} = 75\%$. 9. To write 75 in standard form: $$75 = 7.5 \times 10^1$$ 10. **Summary:** $\frac{3}{4} = 75\% = 7.5 \times 10^1$. This process applies to any fraction or number when converting between these forms.