1. Stating the problem: Convert each decimal number to a fraction or mixed number and simplify. 2. Important rule: To convert a decimal to a fraction, write the decimal without the decimal point as the numerator and use a denominator that is a power of 10 based on the number of decimal places. Then simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). 3. Convert 3.15: - 3.15 = 3 + 0.15 - 0.15 = \frac{15}{100} - Simplify \frac{15}{100} by dividing numerator and denominator by 5: $$\frac{\cancel{15}^3}{\cancel{100}^{20}} = \frac{3}{20}$$ - So, 3.15 = 3 \frac{3}{20} 4. Convert 8.92: - 8.92 = 8 + 0.92 - 0.92 = \frac{92}{100} - Simplify \frac{92}{100} by dividing numerator and denominator by 4: $$\frac{\cancel{92}^{23}}{\cancel{100}^{25}} = \frac{23}{25}$$ - So, 8.92 = 8 \frac{23}{25} 5. Convert 0.6: - 0.6 = \frac{6}{10} - Simplify \frac{6}{10} by dividing numerator and denominator by 2: $$\frac{\cancel{6}^3}{\cancel{10}^5} = \frac{3}{5}$$ 6. Convert 64.39: - 64.39 = 64 + 0.39 - 0.39 = \frac{39}{100} - 39 and 100 have no common divisors other than 1, so fraction is already simplified. - So, 64.39 = 64 \frac{39}{100} 7. Convert 62.83: - 62.83 = 62 + 0.83 - 0.83 = \frac{83}{100} - 83 is prime, so fraction is simplified. - So, 62.83 = 62 \frac{83}{100} 8. Convert 71.4: - 71.4 = 71 + 0.4 - 0.4 = \frac{4}{10} - Simplify \frac{4}{10} by dividing numerator and denominator by 2: $$\frac{\cancel{4}^2}{\cancel{10}^5} = \frac{2}{5}$$ - So, 71.4 = 71 \frac{2}{5}