Math Basics: Numbers, Measurement Systems and Conversions

Rational Numbers

• A rational number is a number that can be expressed as the quotient or fraction of two integers, e.g., 3/4 or 22/7.
• Rational numbers can be expressed in decimal form, which may be finite or infinite and recurring.
• Examples of rational numbers: 0.5, 0.333..., 1.25.

Precision and Accuracy

• Precision: Refers to the closeness of multiple measurements to each other.
• Accuracy: Refers to the closeness of a measurement to its true value.
• A measurement can be precise but not accurate, or accurate but not precise.
• Examples:
  • A person weighing themselves multiple times with the same scale, getting the same reading each time (precise but not accurate if the scale is faulty).
  • A person measuring the length of a room multiple times with different instruments, getting close to the true value (accurate but not precise).

Metric System

• A decimal-based system of measurement.
• Base units:
  • Meter (m) for length
  • Gram (g) for mass
  • Liter (L) for volume
  • Second (s) for time
• Derived units:
  • Velocity: meters per second (m/s)
  • Acceleration: meters per second squared (m/s²)
  • Force: newtons (N)

Converting Between Units

• To convert between units, multiply or divide by the conversion factor.
• Examples:
  • 1 meter = 100 centimeters
  • 1 kilogram = 1000 grams
  • 1 liter = 1000 milliliters

Imperial System

• A system of measurement primarily used in the United States.
• Units:
  • Inch (in) for length
  • Pound (lb) for weight
  • Fluid ounce (fl oz) for volume
• Converting between Imperial and Metric systems:
  • 1 inch ≈ 2.54 centimeters
  • 1 pound ≈ 0.45 kilograms
  • 1 fluid ounce ≈ 30 milliliters