Math Problem Statement

Give me some problems with dimensional analysis sloving with using the giant 1 with answers

Solution

Sure! Here are some dimensional analysis problems that involve using the "Giant 1" technique. The "Giant 1" method helps ensure that units cancel appropriately, leading to a correct solution.

Problem 1: Converting Meters to Feet

Problem: Convert 5 meters to feet. (Use 1 meter=3.28084 feet1 \text{ meter} = 3.28084 \text{ feet})

Solution: 5 meters×3.28084 feet1 meter=16.4042 feet5 \text{ meters} \times \frac{3.28084 \text{ feet}}{1 \text{ meter}} = 16.4042 \text{ feet}

Answer: 16.4042 feet


Problem 2: Converting Kilograms to Pounds

Problem: Convert 10 kilograms to pounds. (Use 1 kg=2.20462 lbs1 \text{ kg} = 2.20462 \text{ lbs})

Solution: 10 kg×2.20462 lbs1 kg=22.0462 lbs10 \text{ kg} \times \frac{2.20462 \text{ lbs}}{1 \text{ kg}} = 22.0462 \text{ lbs}

Answer: 22.0462 lbs


Problem 3: Converting Hours to Seconds

Problem: Convert 3 hours to seconds. (Use 1 hour=3600 seconds1 \text{ hour} = 3600 \text{ seconds})

Solution: 3 hours×3600 seconds1 hour=10800 seconds3 \text{ hours} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} = 10800 \text{ seconds}

Answer: 10800 seconds


Problem 4: Converting Liters to Gallons

Problem: Convert 4 liters to gallons. (Use 1 liter=0.264172 gallons1 \text{ liter} = 0.264172 \text{ gallons})

Solution: 4 liters×0.264172 gallons1 liter=1.056688 gallons4 \text{ liters} \times \frac{0.264172 \text{ gallons}}{1 \text{ liter}} = 1.056688 \text{ gallons}

Answer: 1.056688 gallons


Problem 5: Converting Celsius to Fahrenheit

Problem: Convert 25°C to Fahrenheit. (Use the formula F=95C+32F = \frac{9}{5}C + 32)

Solution: F=95×25+32=45+32=77°FF = \frac{9}{5} \times 25 + 32 = 45 + 32 = 77°F

Answer: 77°F


If you would like further details on any of these problems or have questions, feel free to ask!

Follow-up Questions:

  1. What is the importance of dimensional analysis in physics and engineering?
  2. Can you provide examples of complex conversions that require multiple unit conversions?
  3. How do you apply dimensional analysis to verify equations?
  4. What are some common mistakes to avoid when using dimensional analysis?
  5. How does dimensional analysis help in understanding physical relationships in formulas?

Tip: Always ensure that the units you want to convert to are in the numerator, while the original units are in the denominator to facilitate cancellation.

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Math Problem Analysis

Mathematical Concepts

Dimensional Analysis
Unit Conversion

Formulas

Conversion factor method
F = (9/5)C + 32

Theorems

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Suitable Grade Level

Grades 7-12