Introduction to Physics: Measurement, Units, Prefixes, and Scientific Notation

Introducing Physics

Physical Quantities and Units

Physics is the study of natural phenomena, which involves measurements and equations. In physics, we measure physical quantities such as mass, length, and time. Each measurement must include a number and a unit to be meaningful.

• Physical Quantity: Any property that can be measured (e.g., mass, length, time).

• Unit: A standard quantity used to specify measurements (e.g., kilogram, meter, second).

• Example: Measuring the mass of a box: 10 kilogram (kg)

For equations in physics to work, all units must be compatible with each other. Groups of compatible units form a system of units. In physics, the SI (Système International) units are always used.

Quantity	S.I.	Imperial
Mass	Kilogram (kg)	Pound (lb)
Length	Meter (m)	Foot (ft)
Time	Second (s)	Second (s)
Force	Newton (N)	Foot-pound

Force Equation:

• $F = m \times a$

• Units: $[\text{N}] = [\text{kg}] \times [\text{m}/\text{s}^2]$

• Units must be compatible for equations to be valid.

Measurement Systems and Metric Prefixes

Metric Prefixes

A metric prefix is a letter or symbol that goes before a base unit to indicate a specific power of ten. Prefixes allow us to express very large or very small quantities conveniently.

• Base unit: The fundamental unit (e.g., meter, gram, second).

• Prefix: Indicates multiplication by a power of ten (e.g., kilo-, milli-, micro-).

• Example: $5\,\text{km} = 5 \times 1000 = 5000\,\text{m}$

Power of Ten	Prefix	Symbol
$10^{12}$	tera	T
$10^9$	giga	G
$10^6$	mega	M
$10^3$	kilo	k
$10^2$	hecto	h
$10^1$	deca	da
$10^0$	base unit	-
$10^{-1}$	deci	d
$10^{-2}$	centi	c
$10^{-3}$	milli	m
$10^{-6}$	micro	μ
$10^{-9}$	nano	n
$10^{-12}$	pico	p

Converting Units:

• To convert from a bigger to a smaller unit, the number becomes larger.

• To convert from a smaller to a bigger unit, the number becomes smaller.

• Example: $6.5\,\text{km} = 6,500\,\text{m}$

Steps for Using Metric Prefixes:

1. Identify starting and target prefix.

2. Move from start to target, count # of exponent changes.

3. Shift decimal place in the same direction as exponent change.

Scientific Notation

Purpose and Format

Scientific notation is used to compress very long or very small numbers into a more manageable format. It is especially useful in physics for expressing measurements of large or tiny quantities.

• General Format: $A.BC \times 10^n$ where $1 \leq A < 10$ and $n$ is the exponent.

• Example: Mass of Earth: $5.97 \times 10^{24}\,\text{kg}$

Converting Standard Form to Scientific Notation

• Move decimal point to get a number between 1 and 10.

• Count how many places the decimal moved; this is the exponent.

• If the original number is large, the exponent is positive; if small, the exponent is negative.

• Example: $304,606.27\,\text{kg} = 3.0460627 \times 10^5\,\text{kg}$

Converting Scientific Notation to Standard Form

• If exponent is positive, move decimal right; number becomes larger.

• If exponent is negative, move decimal left; number becomes smaller.

• Example: $5.45 \times 10^5\,\text{kg} = 545,000\,\text{kg}$

Practice Problems and Examples

• Expressing $299,800,000\,\text{m/s}$ in scientific notation: $2.998 \times 10^8\,\text{m/s}$

• Expressing $0.00000529 \times 10^6\,\text{m}$ in scientific notation: $5.299471$

• Expressing $9.98 \times 10^6$ in standard form: $9,980,000$

Summary Table: Key Concepts

Concept	Definition	Example
Physical Quantity	Measurable property	Mass, Length, Time
Unit	Standard for measurement	kg, m, s
Metric Prefix	Symbol for power of ten	kilo-, milli-, micro-
Scientific Notation	Compact form for large/small numbers	$3.0 \times 10^8$

Additional info: These notes cover foundational concepts from Chapter 1: Introducing Physics, including measurement, units, metric prefixes, and scientific notation, which are essential for all subsequent topics in college physics.