Math Problem Statement

Solve the following expression: (57g)(225.56g)(0.112536g) / (1.83L)(0.000034L)(3 * 10^27 L)

Solution

The equation from the image appears to be a complex expression involving multiplication, division, and powers:

(57g)(225.56g)(0.112536g)(1.83L)(0.000034L)(3×1027L)\frac{(57 \, \text{g}) (225.56 \, \text{g}) (0.112536 \, \text{g})}{(1.83 \, \text{L}) (0.000034 \, \text{L}) (3 \times 10^{27} \, \text{L})}

Let's solve this step by step.

  1. Multiply the numerators: 57×225.56×0.112536=value57 \times 225.56 \times 0.112536 = \text{value}
  2. Multiply the denominators: 1.83×0.000034×3×1027=value1.83 \times 0.000034 \times 3 \times 10^{27} = \text{value}
  3. Divide the results from steps 1 and 2: result of step 1result of step 2=final value\frac{\text{result of step 1}}{\text{result of step 2}} = \text{final value}

Let's perform these calculations.The calculation yields the following:

  1. Product of the numerators: 1446.86634912g31446.86634912 \, \text{g}^3
  2. Product of the denominators: 1.8666×1023L31.8666 \times 10^{23} \, \text{L}^3
  3. Final division result: 7.751×1021g3L37.751 \times 10^{-21} \frac{\text{g}^3}{\text{L}^3}

Would you like more details on any part of this solution or do you have any other questions? Here are some related questions you might consider:

  1. How would this result be interpreted in a real-world scenario?
  2. What are the implications of the small result in terms of practical measurements?
  3. How could this equation relate to concentrations or dilutions?
  4. How can significant figures impact the accuracy of this result?
  5. How could the units be simplified or converted for different contexts?

Tip: When working with extremely large or small numbers, especially in scientific contexts, it's important to keep track of the units throughout the calculation to ensure consistency and correctness.

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Math Problem Analysis

Mathematical Concepts

Multiplication
Division
Scientific Notation

Formulas

Multiplication of numerators and denominators
Scientific notation for large numbers

Theorems

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Suitable Grade Level

Grades 9-12