It looks like you're looking to practice approximating values of rational numbers. Here are some tips and examples for approximating rational numbers:
Understanding Rational Numbers
- A rational number is any number that can be expressed as the quotient of two integers \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator (and \( b \neq 0 \)).
Strategies for Approximating
- Decimal Conversion: Convert rational numbers to their decimal form by performing the division.
- Simplification: If the rational number is a fraction, try to simplify it to its lowest terms first.
- Estimating: Determine the proximity to whole numbers or simple fractions for quick estimates.
Examples of Approximating Rational Numbers
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Example 1: \( \frac{7}{8} \)
- Convert to decimal: \( 7 \div 8 = 0.875 \)
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Example 2: \( \frac{3}{4} \)
- Convert to decimal: \( 3 \div 4 = 0.75 \)
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Example 3: \( \frac{5}{6} \)
- Convert to decimal: \( 5 \div 6 \approx 0.833 \) (repeats)
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Example 4: \( \frac{2}{5} \)
- Convert to decimal: \( 2 \div 5 = 0.4 \)
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Example 5: \( \frac{9}{4} \)
- Convert to decimal: \( 9 \div 4 = 2.25 \)
Practice Exercises
Here are some exercises for you to try on your own:
- Approximate \( \frac{10}{3} \).
- Approximate \( \frac{11}{9} \).
- Approximate \( \frac{15}{8} \).
- Approximate \( \frac{4}{7} \).
- Approximate \( \frac{13}{4} \).
Answers to Practice Exercises
- \( \frac{10}{3} \approx 3.33 \)
- \( \frac{11}{9} \approx 1.22 \)
- \( \frac{15}{8} = 1.875 \)
- \( \frac{4}{7} \approx 0.57 \)
- \( \frac{13}{4} = 3.25 \)
Feel free to ask for more examples or clarifications!
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