Study sheet: SI Units and Significant Figures

📋 Course Outline

1. SI System and Base Units
2. Derived Units and Volume
3. Scientific Notation and Prefixes
4. Metric Ladder Conversions
5. Measurement and Significant Figures
6. Significant-Figure Calculations

📖 1. SI System and Base Units

🔑 Key Concepts & Definitions

• International System of Units : a decimal measurement system established by the General Conference of Weights and Measures in 1960

★ Must-know

• The SI base units listed are:
  • meter for length
  • kilogram for mass
  • second for time
  • ampere for electric current
  • kelvin for temperature
  • mole for amount of substance

Further detail

• One meter equals 100 centimeters and 1,000 millimeters.

💡 Memory Hook

Length, mass, time, current, temperature, substance

📖 2. Derived Units and Volume

🔑 Key Concepts & Definitions

• Derived unit : formed by combining SI base units in a calculated quantity

★ Must-know

📐 Formula — Volume is calculated as length multiplied by width multiplied by height: $V = l \times w \times h$.

• The SI unit of volume is the cubic meter, while cubic centimeters are commonly used for solid objects and liters or milliliters for liquids.

Further detail

• One milliliter is equal to one cubic centimeter.

• A graduated cylinder is a suitable device for measuring the volume of a liquid.

💡 Memory Hook

Combining base units → derived quantities

📖 3. Scientific Notation and Prefixes

🔑 Key Concepts & Definitions

• Scientific notation : expresses a large or small number as a number multiplied by a power of ten

★ Must-know

📐 Formula — A positive power of ten is repeated multiplication, $10^n = 10 \times 10 \times \cdots$, while a negative power is its reciprocal, $10^{-n} = \frac{1}{10^n}$.

• The metric prefixes and powers are:
  • tera, 10^12
  • giga, 10^9
  • mega, 10^6
  • kilo, 10^3
  • hecto, 10^2
  • deka, 10^1
  • base unit, 10^0
  • deci, 10^-1
  • centi, 10^-2
  • milli, 10^-3

Further detail

• The number 25,903,000 can be written as $2.5903 \times 10^7$, and 0.000045 can be written as $4.5 \times 10^{-5}$.

💡 Memory Hook

A metric ladder stretching from tera above to atto below the base unit

📖 4. Metric Ladder Conversions

★ Must-know

• 🔄 Metric conversion follows these steps:
  1. Determine the starting unit.
  2. Count the jumps to the ending unit.
  3. Move the decimal point the same number of jumps in the same direction.

Further detail

• Converting 4 kilometers to meters requires three jumps toward the base unit, giving 4,000 meters.

💡 Memory Hook

Start → count jumps → move the decimal

📖 5. Measurement and Significant Figures

🔑 Key Concepts & Definitions

• Significant figures : the digits in a measurement that reflect the measurement's precision

★ Must-know

📌 When recording a measurement, write all certain digits marked by the instrument and estimate one digit beyond the smallest marking.

Further detail

• A measurement of 82.63 grams has four significant figures because 8, 2, and 6 are certain and 3 is estimated.

📌 In 420 grams, the zero is a placeholder rather than a significant figure because the measurement is marked to the hundreds place and estimated to the tens place.

• The value 7,000 has two significant figures when written as 7.0 × 10^3 and four significant figures when written as 7.000 × 10^3.

💡 Memory Hook

Certain digits versus one estimated digit

📖 6. Significant-Figure Calculations

★ Must-know

📌 For addition and subtraction, round the result to the same number of decimal places as the measurement with the fewest decimal places.

📌 For multiplication and division, round the result to the same number of significant figures as the measurement with the fewest significant figures.

Further detail

• The sum 22.75 cm + 98.457 cm + 10.1 cm equals 131.307 cm on a calculator but is reported as 131.3 cm because 10.1 cm has the fewest decimal places.

• The product 0.7 m × 98.457 m equals 68.9199 m² on a calculator but is reported as 70 m² because 0.7 m has the fewest significant figures.

💡 Memory Hook

Addition/subtraction follows decimal places, whereas multiplication/division follows significant figures

📊 Synthesis Tables

Rounding Rules for Calculations

Operation	Rounding basis	Example result
Addition/subtraction	Fewest decimal places	131.3 cm
Multiplication/division	Fewest significant figures	70 m²