Comprehensive Science Measurement and Notation: SI Units, Scientific Notation, and Significant Figures

Measurement

Determining the size of a quantity using a number and a unit

Quantity

The numerical value of a measurement (how much)

Unit

What is being measured (grams, meters, liters, etc.)

Standard Notation

Writing numbers normally (ex: 450, 0.0032)

Scientific Notation

Writing numbers using powers of 10 (ex: 4.5 x 10²)

Coefficient

The number in front of the power of 10 (must be 1-9.9)

Exponent

The power of 10 that shows how many places the decimal moves

Positive Exponent

Used when the number is greater than 1

Negative Exponent

Used when the number is less than 1

Multiplication (Sci) Multiply coefficients, add exponents

Division (Sci)

Divide coefficients, subtract exponents

Addition (Sci)

Exponents must match before adding

Subtraction (Sci)

Exponents must match before subtracting

Significant Figures

Digits we are sure of plus one estimated digit

Uncertainty

Measurements are never exact due to limits of tools

Exact Numbers

Numbers with no uncertainty (ex: conversions)

Nonzero Digits

Always count as significant figures

Zero Between Digits

Always significant (ex: 2806)

Leading Zeros

Not significant (zeros before a number)

Trailing Zeros (Decimal)

Significant if after decimal point

Trailing Zeros (No Decimal)

May or may not be significant

Scientific Notation (Sig Figs)

Used to remove zero confusion

Metric System

Decimal-based measurement system used in science

SI Units:

Standard metric units used internationally

Base Units

Fundamental units used to build other units

Derived Units

Units made from combining base units

Meter (m)

Base unit of length

Kilogram (kg)

Base unit of mass

Second (s)

Base unit of time

Kelvin (K)

Base unit of temperature

Mole (mol)

Unit for amount of substance

Liter (L)

Common unit of volume in chemistry

Milliliter (mL)

One-thousandth of a liter

Kilo (k)

One thousand (10³)

Centi (c)

One hundredth (10⁻²)

Milli (m)

One-thousandth (10⁻³)

Micro (µ)

One-millionth (10⁻⁶)

Nano (n)

One-billionth (10⁻⁹)

Dimensional Analysis

Method using units to guide conversions

Conversion Factor

A ratio used to change units

Equivalency

Statement that two values are equal in different units

Unit Cancellation

Units cancel out during conversion

Metric Conversion

Moving decimal based on prefix