Case Study: The Solar Power Plant
A new solar farm is being built. The engineers are calculating the energy output and costs using specific "patterns of \(10\)" to make their planning faster.
Each solar panel produces 500 watts of energy per hour.
The farm is organized into "Blocks" of \(10\) panels, "Arrays" of \(100\) panels, and "Fields" of \(1,000\) panels.
Multiplication Patterns (Powers of \(10\)):
1. The Power Increase: If \(1\) panel produces 500 watts, use the multiplication pattern to find the output of:
\(10\) panels (\(1\) Block): \(500 \times 10 =\) watts.
\(100\) panels (\(1\) Array): \(500 \times 100 =\) watts.
\(1,000\) panels (\(1\) Field): \(500 \times 1,000 =\) watts.
2. Pattern Observation: When multiplying a whole number by \(10, 100,\) or \(1,000\) what happens to the number of zeros at the end of the product?
3. The Costing Pattern: The cost of cleaning one panel is ₹43. Look at the pattern below and fill in the missing value for the cost of cleaning an entire Field (\(1,000\) panels).
\(1\) Panel: ₹ 43
\(10\) Panels: ₹ 43\(0\)
\(100\) Panels: ₹
\(1,000\) Panels: ₹
4. Missing Factor: If the total energy of a specific section is 25000 watts and each panel provides 500 watts, how many panels are in that section? (Hint: \(500 \times ? =25000\))