Subjects algebra

Compare Rationals 97Eac1

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1. **Stating the problem:** We are given two rational numbers: 0.650 and \( \frac{13}{20} \). We need to determine which of the following statements is true: 1. \(0.650 > \frac{13}{20}\) 2. \(0.650 < \frac{13}{20}\) 3. \(0.650 = \frac{13}{20}\) 2. **Formula and approach:** To compare a decimal and a fraction, convert the fraction to a decimal or the decimal to a fraction. Here, we convert \( \frac{13}{20} \) to decimal by dividing numerator by denominator: $$ \frac{13}{20} = 13 \div 20 $$ 3. **Calculating the decimal value of \( \frac{13}{20} \):** $$ 13 \div 20 = 0.65 $$ 4. **Comparing the two numbers:** Given decimal: 0.650 Fraction as decimal: 0.65 Note that 0.650 and 0.65 represent the same number because trailing zeros after the decimal point do not change the value. 5. **Conclusion:** \(0.650 = 0.65 = \frac{13}{20}\) Therefore, statement 3 is true. **Final answer:** \(0.650 = \frac{13}{20}\)