Difficulty: Foundational | Prerequisites: None
Chemistry uses the SI system (metres, kilograms, seconds, kelvin, moles) as its measurement backbone, with metric prefixes scaling units up or down by powers of ten. Significant figures tell you how precise a measured value is, and the Pacific Atlantic Rule is a quick way to spot which zeros count. Scientific notation, dimensional analysis, and the precision-vs-accuracy distinction round out the toolkit you need before touching any calculation in this course.
SI base units
The International System of Units defines seven fundamental quantities, five of which matter for general chemistry: time (second), length (metre), mass (kilogram), temperature (kelvin), and amount of substance (mole).
In simple terms, these are the five "building block" units everything else in chemistry is measured from.
Derived units
Units built by combining base units to measure quantities that have no base unit of their own, such as volume (m³) or density (kg/m³).
Think of it as: you multiply or divide base units together to get a new unit for a new kind of measurement.
Significant figures (sig figs)
The digits in a measured value that carry meaning about the precision of the measurement. All non-zero digits are significant; zeros may or may not be, depending on their position.
In simple terms, sig figs tell you how trustworthy a number is. More sig figs means the measurement was more precise.
Pacific Atlantic Rule
A mnemonic for counting significant figures. "Pacific" (decimal point Present): count from the left, starting at the first non-zero digit. "Atlantic" (decimal point Absent): count from the right, starting at the first non-zero digit.
Think of it as: if there is a decimal point, start from the Pacific (left) side of a US map. If the decimal is absent, start from the Atlantic (right) side.
Scientific notation
A way of expressing very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of 10. In chemistry, the convention is to write numbers to three significant digits.
In simple terms, instead of writing out all the zeros, you write one tidy number times 10 raised to some power.
Dimensional analysis
A problem-solving method that uses conversion factors to cancel unwanted units and arrive at the desired units. Sometimes called the factor-label method or unit-factor method.
Think of it as: set up fractions so the units you want to get rid of cancel out, and you are left with the units you need.
Precision
How close a series of measurements are to each other. High precision means repeated measurements cluster tightly together, regardless of whether they are near the true value.
In simple terms, precision is about consistency. If you weigh something five times and get 5.01, 5.02, 5.01, 5.02, 5.01, that is precise.
Accuracy
How close a measurement is to the true (accepted) value. A measurement can be accurate without being precise, and vice versa.
In simple terms, accuracy is about being correct. If the true mass is 5.00 g and you get 5.01 g, that is accurate.
Base Quantity | Base Unit |
|---|---|
Time | Second (s) |
Length | Metre (m) |
Mass | Kilogram (kg) |
Temperature | Kelvin (K) |
Amount of substance | Mole (mol) |
Derived units combine these. Volume is m³ (the litre is a convenient shorthand for 1 dm³), and density is mass over volume, typically kg/m³.
Factor | Prefix | Example |
|---|---|---|
10⁹ | giga- | gigametre |
10⁶ | mega- | megagram |
10³ | kilo- | kilometre |
10¹ | deca- | decalitre |
10⁻¹ | deci- | decilitre |
10⁻² | centi- | centimetre |
10⁻³ | milli- | milligram |
10⁻⁶ | micro- | microgram |
10⁻⁹ | nano- | nanometre |
10⁻¹⁰ | angstrom | Å |
10⁻¹² | pico- | picometre |
All non-zero digits are significant.
Zeros between non-zero digits ("captive zeros") are significant.
Pacific Atlantic Rule: if a decimal point is present, count from the left (Pacific side), starting at the first non-zero digit. If a decimal point is absent, count from the right (Atlantic side), starting at the first non-zero digit.
5,000,000 has 1 significant figure (no decimal, the trailing zeros are insignificant).
0.000000005 has 1 significant figure (decimal present, the leading zeros are insignificant).
Rounding with trailing zeros (banker’s rounding):
When the digit to be dropped is exactly 5 and followed only by zeros, round to the nearest even number.
2.5350 rounds to 2.54 (the 3 is odd, so it rounds up).
2.5250 rounds to 2.52 (the 2 is even, so it stays).
Write a number as a coefficient between 1 and 10, multiplied by 10 raised to an integer power.
Chemistry convention: express numbers to three significant digits.
Moving the decimal to the left increases the exponent; moving it to the right decreases it.
Set up a chain of conversion factors so that unwanted units cancel and you are left with the target unit.
Example: to convert x units into seconds, given a rate of 1 second per 1 unit:
x units × (1 second / 1 unit) = x seconds
The "units" label cancels, leaving "seconds."
Precision: measurements cluster close to each other (repeatable).
Accuracy: measurements cluster close to the true value (correct).
A dataset can be precise but inaccurate (consistently wrong), or accurate but imprecise (scattered around the true value).
When graphing data, plot the independent variable on the x-axis and the dependent variable on the y-axis, then look for trends in the relationship.
Sig fig rules for arithmetic:
Multiplication and division: the answer has the same number of significant figures as the measurement with the fewest sig figs.
Addition and subtraction: the answer has the same number of decimal places as the measurement with the fewest decimal places.
Dimensional analysis setup:
Given value × (desired unit / given unit) = answer in desired units
Chain as many conversion factors as needed; every unwanted unit must cancel.
Significant figures matter whenever you read an instrument in a lab: the last digit of every measurement is always an estimate, and sig figs capture that uncertainty. Dimensional analysis is the same technique engineers use when converting between imperial and metric specs on blueprints. Precision and accuracy are the reason pharmaceutical companies run the same assay dozens of times: they need results that are both repeatable (precise) and correct (accurate).
Students often think all zeros are insignificant. They are not. Captive zeros (zeros between non-zero digits, e.g. 1,003) are always significant.
Students often confuse precision with accuracy. A set of measurements can be very precise (tightly clustered) yet completely inaccurate (far from the true value). The two are independent.
Students often round 2.5 up to 3 in every case. In chemistry, banker’s rounding applies when the trailing digit is exactly 5 followed by zeros: round to the nearest even digit, not always up.
Students often think scientific notation changes the number of significant figures. It does not. 5.00 × 10³ has three sig figs, the same as 5,000. written with a decimal (5.00 × 10³ is just a cleaner way to show it).
⚠️ The Pacific Atlantic Rule is a favourite exam question. Expect a number like 0.00420 or 30,200 and be asked to state the number of significant figures.
⚠️ Dimensional analysis problems often appear as multi-step unit conversions (e.g. miles to kilometres via inches and centimetres). Set up your conversion factors before you touch the calculator.
⚠️ Precision vs. accuracy: expect a dart-board style diagram or a table of repeated measurements and be asked to classify the dataset.
⚠️ Rounding with the trailing-zero rule (banker’s rounding) comes up as a gotcha in calculation problems.
True or False: 0.00370 has three significant figures.
True or False: Precision and accuracy mean the same thing.
Fill in the blank: In scientific notation, the coefficient must be between ___ and ___.
True or False: When multiplying, the answer takes the fewest decimal places of the inputs.
Fill in the blank: The SI base unit for amount of substance is the ___.
Answers: 1. True (3, 7, 0 are significant). 2. False. 3. 1 and 10. 4. False (it takes the fewest significant figures, not decimal places; decimal places apply to addition/subtraction). 5. Mole.
Q: How many significant figures are in 0.004050?
A: Four. The leading zeros are not significant (Pacific rule, decimal present, count from the left starting at the first non-zero digit: 4, 0, 5, 0).
Q: Convert 3.50 km to centimetres using dimensional analysis.
A: 3.50 km × (1,000 m / 1 km) × (100 cm / 1 m) = 350,000 cm, or 3.50 × 10⁵ cm (three sig figs).
Q: A student measures the mass of a sample five times and gets 4.52 g, 4.53 g, 4.51 g, 4.52 g, 4.53 g. The accepted value is 4.80 g. Is the dataset precise, accurate, both, or neither?
A: Precise but not accurate. The measurements are tightly clustered (good precision) but far from the true value of 4.80 g (poor accuracy).
Q: Round 3.4650 to three significant figures using the trailing-zero (banker’s) rounding rule.
A: 3.46. The digit after the 6 is 5 followed by a zero. The 6 is even, so it stays. The answer is 3.46.
Q: Express 0.0000728 in scientific notation to three significant digits.
A: 7.28 × 10⁻⁵.
Significant figures and dimensional analysis reappear in every quantitative chapter of the course: stoichiometry calculations, molar mass work, gas law problems, and solution concentration all rely on correct sig fig handling and unit conversions. Precision and accuracy connect directly to the lab component, where you will calculate percent error (actual vs. expected value) and percent yield.
SI units, metric system, base units, derived units, significant figures, sig figs, significant digits, Pacific Atlantic Rule, Pacific Atlantic mnemonic, scientific notation, powers of ten, dimensional analysis, factor-label method, unit conversion, precision, accuracy, precision vs accuracy, banker’s rounding, rounding to even, metric prefixes, giga, mega, kilo, centi, milli, micro, nano, pico, angstrom, general chemistry, Purdue, CHM, midterm review