Math Problem Statement

What are the units for the converted rate?

Solution

To determine the correct units for the converted rate in this problem, let’s analyze the unit conversions step-by-step:

  1. Initial Units: Starting with 2miles2 \, \text{miles}.
  2. First Conversion: Multiply by 5280feet1mile\frac{5280 \, \text{feet}}{1 \, \text{mile}} to convert miles to feet. The "miles" units cancel out, leaving us with feet.
  3. Second Conversion: Multiply by 12inches1foot\frac{12 \, \text{inches}}{1 \, \text{foot}} to convert feet to inches. The "feet" units cancel out, leaving us with inches.

After these conversions, we’re left with inches as the final unit.

Answer

The correct answer is:

  • inches

Would you like a detailed explanation of each conversion step or have any questions?


Here are five related questions to expand your understanding:

  1. What is the purpose of canceling units in dimensional analysis?
  2. How would the answer change if we started with 2 miles per hour?
  3. How can we convert inches back to miles?
  4. What are some practical applications of unit conversion in daily life?
  5. How would you convert square miles to square inches?

Tip:

Always track units carefully in each step of a calculation to ensure accuracy, especially in multi-step conversions.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Dimensional Analysis

Formulas

1 mile = 5280 feet
1 foot = 12 inches

Theorems

Dimensional Analysis

Suitable Grade Level

Grades 6-8