Math Problem Statement

What is the % difference between 1,099,009 and 1,023,259?

Solution

To calculate the percentage difference between two numbers, we use the formula:

Percentage Difference=Value1Value2Average of the Two Values×100\text{Percentage Difference} = \frac{\lvert \text{Value}_1 - \text{Value}_2 \rvert}{\text{Average of the Two Values}} \times 100

Where the average of the two values is:

Average=Value1+Value22\text{Average} = \frac{\text{Value}_1 + \text{Value}_2}{2}

Given: Value1=1,099,009andValue2=1,023,259\text{Value}_1 = 1,099,009 \quad \text{and} \quad \text{Value}_2 = 1,023,259

Step-by-Step Solution:

  1. Find the difference between the two values: Difference=1,099,0091,023,259=75,750\text{Difference} = \lvert 1,099,009 - 1,023,259 \rvert = 75,750

  2. Find the average of the two values: Average=1,099,009+1,023,2592=2,122,2682=1,061,134\text{Average} = \frac{1,099,009 + 1,023,259}{2} = \frac{2,122,268}{2} = 1,061,134

  3. Calculate the percentage difference: Percentage Difference=75,7501,061,134×1007.14%\text{Percentage Difference} = \frac{75,750}{1,061,134} \times 100 \approx 7.14\%

So, the percentage difference is approximately 7.14%.

Would you like further details or have any questions? Here are 5 related questions you might find interesting:

  1. How is percentage difference different from percentage change?
  2. Can you calculate the percentage change from 1,023,259 to 1,099,009?
  3. How would rounding affect the accuracy of percentage difference?
  4. What are the real-world applications of percentage difference?
  5. How can I use this formula in complex datasets?

Tip: Always remember to use absolute values when calculating percentage difference, as it measures the magnitude, not the direction!

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Percentage Difference
Absolute Value

Formulas

Percentage Difference = (|Value1 - Value2| / Average of the Two Values) × 100
Average = (Value1 + Value2) / 2

Theorems

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Suitable Grade Level

Grades 9-11