Physics SF, Phy Quantities 1.1

1. Significant Figures

Significant figures the total number of certain digits in a measured value, including the last uncertain digit.

1.1 Reasons for Importance

  • indicate the precision of a measurement or result

  • prevents overstating accuracy in calculations

  • maintains consistency while reporting scientific data

1.2 Rules

  1. non zero numbers are always significant (20→2; 10000→1)

  2. 0s between non zero numbers are significant (1001→4)

  3. leading zeroes are never significant (001→1)

  4. trailing zeroes before a decimal place are insignificant but after a dp are significant (1010→3; 1010.0 → 5)

  5. all specific values have unlimited SF (numbers like 1m=100cm can be rewritten as 100.00000 infinitely)

2. Significant Figures in Calculations

When performing calculations, the result's precision must reflect the precision of the input measurements.

So if 1.0kg has to be converted to grams, it can be 1.0×10³ grams.

if 1.23 kg has to be converted to grams, it can be 1230g or 123×10, or 12.3×10², or 1.23×10³

  • Addition and Subtraction:

    • The result will have the least number of decimal places as per the given data.

    • 1.10+1.2= 2.2

    • 3.996+4.0 = 7.996 → 8.0 (round off to the minimum sf (2sf))

  • Multiplication and Division:

    • The result will have the least order of significant figures as compared to the given data.

    • 1.01×3=3.03→3

    • 9.16×400.0 = 3.664 → 3.6

  • Relaxation (IGCSE Paper 2/4): Examiners may accept two decimal places by default as a standard, even if it deviates from the strict rules of significant figures.

3. Physical Quantities

Physical Quantities have a magnitude and unit (inverse relation, if unit reduces (m→cm) magnitude increases (1→100)

Units are essential for defining quantities and ensuring consistent measurements.

  • Fundamental Units:

    • Units that cannot be broken down further (e.g., meter for length, second for time).

    • Example: Meter is fundamental because it defines length on its own.

    • Length (m), Time (s), Mass (kg), Temperature (K), Current (A), Brightness (Cd), Amount (Mol)

  • Derived Units:

    • Units formed by combining fundamental units.

    • Examples: Velocity, force, density, power, energy, volume.

    • Velocity requires both meter (length) and second (time).

  • Cube → V=s³; SA=6s²
    Cuboid → V=lbh; SA=2(lb+bh+hl)
    Sphere → V=4πr³/3, SA=4πr²
    Cone → V=πr²h/3, SA=πr(r+l)
    Cylinder → V=πr²h, SA=2πr(r+h)