1.3 Estimation of physical quantities

• The method of rounding involves approximating a value to the nearest whole number or decimal
• One purpose of estimation is to plan experiments effectively by gauging expected results
• The order of magnitude of the Earth's mass is 10^24 kg
• Order of magnitude estimates the scale of a quantity by identifying its power of 10.


  True
• The mass of the Earth is on the order of 10^24
• Rounding involves approximating a value to the nearest whole number, decimal place, or significant figure
• Order the steps for solving a Fermi problem:

  1️⃣ Break down the problem into sub-questions

  2️⃣ Make reasonable assumptions

  3️⃣ Estimate values for variables

  4️⃣ Calculate the final result
• Estimation is generally faster but has lower accuracy
• How many significant figures are in the number 3.45?

  Three
• Steps to solve a Fermi problem

  1️⃣ Break down the problem into sub-questions

  2️⃣ Make reasonable assumptions

  3️⃣ Estimate values using known constants

  4️⃣ Convert units to the same scale

  5️⃣ Calculate by multiplying estimated values

  6️⃣ Verify if the estimate aligns with expectations
• The final step in solving a Fermi problem is to verify the calculated estimate.


  True
• The number of significant figures in 3.450 is three.

  False
• What does the term "order of magnitude" refer to in estimation?

  Power of 10
• The number 3.45 has three significant figures.


  True
• Data gaps in estimation refer to the lack of precise details, leading to approximate values.


  True
• Match the limitation with its description:

  Assumptions ↔️ Based on initial estimates that may be inaccurate

  Data Gaps ↔️ Lacks detailed data, leading to approximate values

  Simplified Models ↔️ Uses basic models that omit complex factors
• Estimation is vital in physics for quick verification
• What is the order of magnitude of the Earth's mass in kilograms?

  $10^{24}$
• Steps for solving a Fermi problem

  1️⃣ Break down the problem

  2️⃣ Make assumptions

  3️⃣ Estimate values

  4️⃣ Convert units

  5️⃣ Calculate

  6️⃣ Verify the result
• Significant figures express the precision of a measurement.


  True
• Significant figures express the precision of a measurement by counting the meaningful digits
• What tools are used for estimation in physics?

  Mental calculations, reference tables
• Order of magnitude estimates the scale of a quantity by identifying its power of 10.


  True
• Estimation in physics uses intuition rather than precise measurements.


  True
• Exact measurements rely on approximations and intuition.

  False
• In order of magnitude, the mass of the Earth is estimated as $10^{24}$ kg
• Exact measurements are faster than estimations.

  False
• Estimation helps in understanding the relative magnitudes of quantities.


  True
• What is the estimated number of grains of sand on a beach with dimensions 1 km x 100 m x 1 m and a sand grain size of 0.1 mm?

  $10^{15}$
• Rounding involves approximating a value to the nearest whole number, decimal place, or significant figure
• Order the following features to compare estimation and exact measurements:

  1️⃣ Purpose: Quick verification vs. accuracy | precision

  2️⃣ Method: Approximations vs. precise procedures

  3️⃣ Accuracy: Lower vs. higher

  4️⃣ Time: Faster vs. slower
• Match the estimation feature with its corresponding characteristic:

  Purpose ↔️ Quick verification, planning

  Method ↔️ Approximations, intuition

  Accuracy ↔️ Lower

  Time ↔️ Faster
• Why is estimating physical quantities important in physics?

  Quick verification, planning
• Match the purpose of estimation with its description:

  Quick Verification ↔️ Check if calculations make sense

  Experimental Design ↔️ Plan experiments effectively

  Understanding Scale ↔️ Provide context for magnitudes
• What does the rounding method involve in estimation?

  Approximating to nearest value
• Estimating the scale of a quantity by identifying its power of 10 is called order of magnitude.
• Fermi problems involve breaking a complex question into smaller, manageable steps.
• What is the estimated size of a sand grain in millimeters for a Fermi problem?

  0.1 mm
• What is the order of magnitude of the Earth's mass in kilograms?

  $10^{24}$
• When rounding 3.14159 to three significant figures, the result is 3.14.