Unit 3B: Putting Numbers in Perspective

Scientific Notation

• A number expressed as a value between 1 and 10 multiplied by a power of 10.

Perspective through Estimation

• Order of Magnitude Estimate: A broad value range, typically within one or two powers of ten (e.g., "in the ten thousands" or "in the millions").

Examples of Perspective

• Ice Cream Spending: Estimation helps gauge total annual ice cream spending in the U.S. based on average servings.

Energy Comparisons (Table 3.1)

• Metabolism of Candy Bar: $1 × 10^6$ joules

• 1 Hour of Running (Adult): $4 × 10^6$ joules

• 1 Liter of Oil: $1.2 × 10^{7}$ joules

• Average Daily Electrical Energy Use: $5 × 10^{7}$ joules

• 1 Kg of Coal Burned: $1.6 × 10^{10}$ joules

• 1 Kg of Uranium-235: $5.6 × 10^{13}$ joules

• Hydrogen Fusion (1 liter of water): $6.9 × 10^{13}$ joules

• U.S. Annual Energy Consumption: $1.0 × 10^{20}$ joules

• World Annual Energy Consumption: $5.3 × 10^{20}$ joules

• Annual Energy Generation of Sun: $1 × 10^{34}$ joules

Comparison of U.S. vs. World Energy Consumption

• Analyzes population and energy usage differences between the U.S. and the world.

Scaling Perspectives

• Verbal Scaling: "1 cm = 1 km"

• Graphical Scaling: Scale ratio of 1:100,000.

Earth and Sun Perspective

• Distance from Earth to Sun: ~150 million km.

• Sun diameter: ~1.4 million km.

• Earth equatorial diameter: ~12,760 km.

• Scale model of solar system example with a 1 to 10 billion scale.

Case Study: What is a Billion Dollars?

• Question posed: How many people could be employed with $1 billion/year at $200,000 total cost per employee? 9