Math Basics: Numbers, Measurement Systems and Conversions

Study Notes

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

Description

Test your understanding of rational numbers, precision and accuracy, the metric system, converting between units, and the imperial system. Learn the definitions, examples, and conversion factors to become proficient in math basics.