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For Problems 20-25, compare the measurements using \( <_{1}= \), or \( > \). 20. 2 meters \( \square \) 7 feet 21. 50 pounds \( \square \) 25 kilograms 22. 100 inches \( \square \) 254 centimeters 23. 10 miles \( \square \) 6.2 kilometers 24. 6 liters \( \square \) 2 gallons 25. 24 ounces \( \square \) 600 grams

Ask by Goodwin Murphy. in the United States
Jan 22,2025

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Answer

20. 2 meters < 7 feet 21. 50 pounds < 25 kilograms 22. 100 inches = 254 centimeters 23. 10 miles > 6.2 kilometers 24. 6 liters < 2 gallons 25. 24 ounces > 600 grams

Solution

Sure, let's compare each pair of measurements using \( < \), \( = \), or \( > \). ### 20. 2 meters \( \square \) 7 feet - **Conversion:** \( 1 \) meter ≈ \( 3.28084 \) feet \( 2 \) meters ≈ \( 6.56168 \) feet - **Comparison:** \( 6.56168 \) feet < \( 7 \) feet - **Result:** \( 2 \) meters **\( < \)** \( 7 \) feet ### 21. 50 pounds \( \square \) 25 kilograms - **Conversion:** \( 1 \) kilogram ≈ \( 2.20462 \) pounds \( 25 \) kilograms ≈ \( 55.1155 \) pounds - **Comparison:** \( 50 \) pounds < \( 55.1155 \) pounds - **Result:** \( 50 \) pounds **\( < \)** \( 25 \) kilograms ### 22. 100 inches \( \square \) 254 centimeters - **Conversion:** \( 1 \) inch = \( 2.54 \) centimeters \( 100 \) inches = \( 254 \) centimeters - **Comparison:** \( 254 \) centimeters \( = \) \( 254 \) centimeters - **Result:** \( 100 \) inches **\( = \)** \( 254 \) centimeters ### 23. 10 miles \( \square \) 6.2 kilometers - **Conversion:** \( 1 \) mile ≈ \( 1.60934 \) kilometers \( 10 \) miles ≈ \( 16.0934 \) kilometers - **Comparison:** \( 16.0934 \) kilometers > \( 6.2 \) kilometers - **Result:** \( 10 \) miles **\( > \)** \( 6.2 \) kilometers ### 24. 6 liters \( \square \) 2 gallons - **Conversion (US gallons):** \( 1 \) gallon = \( 3.78541 \) liters \( 2 \) gallons = \( 7.57082 \) liters - **Comparison:** \( 6 \) liters < \( 7.57082 \) liters - **Result:** \( 6 \) liters **\( < \)** \( 2 \) gallons ### 25. 24 ounces \( \square \) 600 grams - **Conversion:** \( 1 \) ounce = \( 28.3495 \) grams \( 24 \) ounces = \( 680.388 \) grams - **Comparison:** \( 680.388 \) grams > \( 600 \) grams - **Result:** \( 24 \) ounces **\( > \)** \( 600 \) grams --- **Summary of Comparisons:** 20. \( 2 \) meters **\( < \)** \( 7 \) feet 21. \( 50 \) pounds **\( < \)** \( 25 \) kilograms 22. \( 100 \) inches **\( = \)** \( 254 \) centimeters 23. \( 10 \) miles **\( > \)** \( 6.2 \) kilometers 24. \( 6 \) liters **\( < \)** \( 2 \) gallons 25. \( 24 \) ounces **\( > \)** \( 600 \) grams

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Extra Insights

When converting between different units of measurement, it's all about knowing the right conversion factors. For example, 1 meter is approximately 3.281 feet, so you would multiply 2 meters by that factor to help determine its equivalence in feet. Familiarizing yourself with these factors is key to comparing various measurements accurately—just a small mistake can lead you astray! Additionally, always double-check your calculations by converting back to the original unit if possible. It’s easy to misplace a decimal or mix up units. A common pitfall is forgetting that there are different quantities for the same unit—like pounds versus kilograms or ounces versus grams—which can lead to errors. Keeping track of unit consistency is essential, so keep a handy conversion chart nearby while you're practicing!

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