Physical Quantities

🎯 Class Objective:

Applies unit conversions and scientific notation to physical quantities and evaluates the validity of base-10 scaling analogies to check consistency in measurement representations.

📏 Physical Quantities – Scientific Notation – Conversions

A. Scientific Notation Mastery

1. Express in scientific notation:
   
   

a) 0.00000082
b) 4,560,000
c) 0.00340
d) 9.81
e) 120,000,000

2. Convert to standard form:
   
   

a) 7.2 × 10⁵
b) 3.6 × 10⁻⁴
c) 1.02 × 10³
d) 9.9 × 10⁻²

3. Perform operations (write answer in scientific notation):
   
   

a) (3.0 × 10³) (2.0 × 10²)
b) (4.5 × 10⁶) / (1.5 × 10²)
c) (6.0 × 10⁴) + (2.0 × 10⁴)

B. Conversion Consistency Check

1. Convert:
   
   

a) 72 km/h to m/s
b) 0.45 kg to g
c) 2500 m to km
d) 3.2 h to seconds

2. A student writes:
   
   

15 m = 1500 cm = 0.015 km

Is this correct? Identify and correct the mistake.

3. Explain why scientific notation reduces conversion errors when working with extreme magnitudes.
   
   

C. Scaling Logic

1. If length increases by 10², how does area change?
   
   

2. If mass decreases by 10³, what happens to its scientific notation exponent?
   
   

3. A value changes from 4.5 × 10² to 4.5 × 10⁻³.
   By what factor did it change?

➕ Vectors and Operations

A. Scalar or Vector?

Classify and justify:

• Distance
  
  

• Displacement
  
  

• Speed
  
  

• Velocity
  
  

• Time
  
  

• Acceleration
  
  

• Force
  
  

B. Vector Addition

1. A person walks:
   
   

• 4 m East
  
  

• 3 m North
  
  

Find:

a) Resultant magnitude
b) Direction (angle)

2. A vector A = (6, 8).
   Find magnitude and direction.