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.
Fractions Percentages 78D308
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