Difficulty: Introductory | Prerequisites: None
This covers the practical side of chemistry: how to convert units, handle significant figures in both measurements and calculations, use the density formula, measure volumes in the lab, and understand electronegativity trends on the periodic table. These skills come up in nearly every problem set and exam in the course.
Every chemistry calculation lives or dies by correct units and the right number of significant figures. Density links mass to volume (Volume = Mass / Density), and knowing electronegativity trends on the periodic table tells you which atom pulls harder on shared electrons in a bond. These are the mechanical skills that show up in every problem set.
Significant figures (sig figs)
The digits in a measurement that carry meaning about its precision. In simple terms, they tell you how confident you can be in a measured value.
Leading zeros
Zeros that appear before the first non-zero digit in a decimal number (e.g. 0.0038). They are not significant; they are just placeholders.
Trailing zeros
Zeros at the end of a number. In a decimal number (e.g. 5.00), they are significant. In a whole number without a decimal point (e.g. 500), they may or may not be significant.
Density
Mass per unit volume, typically expressed in g/cm³ or g/mL. Think of it as how tightly packed the matter is.
Electronegativity
A measure of an atom's ability to attract shared electrons in a chemical bond. Higher electronegativity means a stronger pull on electrons.
Graduated cylinder
A piece of laboratory glassware used to measure liquid volumes. Always read at the bottom of the meniscus, at eye level.
Precision
How close repeated measurements are to one another. A precise set of measurements clusters tightly, whether or not the cluster is near the true value.
Accuracy
How close a measurement is to the true or accepted value. You can be precise without being accurate, and vice versa.
1 metre = 100 centimetres.
To convert metres to centimetres, multiply by 100.
3.5 m × 100 = 350 cm.
To convert centimetres to metres, divide by 100.
Dimensional analysis (multiplying by a conversion factor equal to 1) is the safest way to handle any unit conversion.
All non-zero digits are significant.
Zeros between non-zero digits are significant (e.g. 1002 has 4 sig figs).
Leading zeros are never significant (e.g. 0.0038 has 2 sig figs).
Trailing zeros in a decimal number are significant (e.g. 5.00 has 3 sig figs).
Example: 0.038692836 rounded to 6 significant figures is 0.038693.
For multiplication and division: the answer has the same number of sig figs as the measurement with the fewest sig figs.
For addition and subtraction: the answer has the same number of decimal places as the measurement with the fewest decimal places.
Worked example: 0.6931 + 8.98 + (2.0 × 2.45)
2.0 × 2.45 = 4.9 (2 sig figs, limited by 2.0).
Sum: 0.6931 + 8.98 + 4.9 = 14.5731.
Rounded to 2 significant figures: 14 (limited by the 4.9 term, which has the fewest sig figs in the final addition when following the combined rule).
Density = Mass / Volume, rearranged to Volume = Mass / Density.
1 cm³ = 1 mL (this equivalence comes up constantly).
Example: a 39 g sample with density 7.8 g/cm³ has a volume of 39 / 7.8 = 5.0 mL.
Read a graduated cylinder at eye level, at the bottom of the meniscus.
Record the initial volume before removing any liquid.
Subtract the amount removed to find the final volume.
Initial: 43.0 mL. Removed: 7.0 mL. Final: 36.0 mL.
Electronegativity increases across a period (left to right) because nuclear charge increases while atomic radius decreases.
Electronegativity decreases down a group because the valence electrons are farther from the nucleus and more shielded.
Fluorine is the most electronegative element. Francium is the least.
Electronegativity differences between bonded atoms determine bond polarity: large difference = ionic, small difference = polar covalent, near zero = nonpolar covalent.
Density formula
Density = Mass / Volume
Volume = Mass / Density
Mass = Density × Volume
Unit conversion factor (metres to centimetres)
1 m = 100 cm, so the conversion factor is (100 cm / 1 m) or (1 m / 100 cm).
Significant figures rules summary
Operation | Rule |
|---|---|
Multiplication / division | Match the fewest sig figs among the inputs |
Addition / subtraction | Match the fewest decimal places among the inputs |
Counting numbers and exact definitions | Infinite sig figs (do not limit your answer) |
Significant figures matter everywhere measurements matter: a pharmacist dispensing medication, an engineer tolerancing a part, a chemist titrating a solution. Density is how jewellers distinguish real gold from fakes (gold is 19.3 g/cm³, much denser than most substitutes). Electronegativity trends explain why water is polar (oxygen pulls electrons away from hydrogen), which in turn explains most of water's unusual properties.
Students often think leading zeros are significant. They are not. In 0.0038, only the 3 and 8 count.
Students sometimes round intermediate steps instead of rounding only the final answer. Premature rounding introduces error; carry extra digits through your working and round once at the end.
Students often confuse precision with accuracy. A set of measurements can be very precise (tightly clustered) but inaccurate (far from the true value) if there is a systematic error.
Students sometimes think electronegativity increases down a group because atomic number increases. The opposite is true: electronegativity decreases down a group because the valence shell is farther from the nucleus.
⚠️ Significant figures questions appear on nearly every exam. Know the four rules (non-zero digits, captive zeros, leading zeros, trailing zeros) cold.
⚠️ Density problems are quick marks if you can rearrange the formula. Expect to go from mass and density to volume, or from mass and volume to density.
⚠️ Electronegativity trend questions often ask you to identify the least or most electronegative element in a set. Remember: bottom-left of the periodic table is lowest (francium), top-right is highest (fluorine, excluding noble gases).
⚠️ Lab measurement questions test whether you know to read the graduated cylinder at the meniscus and at eye level.
Fill in the blank: 0.00420 has ______ significant figures. (3.)
True or false: Leading zeros are significant. (False.)
Fill in the blank: Volume = ______ / ______. (Mass / Density.)
True or false: Electronegativity increases down a group. (False: it decreases.)
Fill in the blank: 1 cm³ = ______ mL. (1.)
Q: Convert 3.5 metres to centimetres.
A: 3.5 × 100 = 350 cm.
Q: How many significant figures are in 0.038692836?
A: 7 significant figures (3, 8, 6, 9, 2, 8, 3, 6). The leading zeros are not significant.
Q: Round 0.038692836 to 6 significant figures.
A: 0.0386928 rounded to 6 sig figs is 0.038693 (the 2 rounds up to 3 because the next digit is 8).
Q: Calculate the result of 0.6931 + 8.98 + (2.0 × 2.45) and express it with the correct number of significant figures.
A: 2.0 × 2.45 = 4.9 (2 sig figs). Sum: 0.6931 + 8.98 + 4.9 = 14.5731. Rounded to 2 sig figs: 15 (the least precise term, 4.9, has 2 sig figs).
Q: A sample has a mass of 39 g and a density of 7.8 g/cm³. What is its volume in mL?
A: Volume = 39 / 7.8 = 5.0 mL (since 1 cm³ = 1 mL).
Q: You have 43.0 mL of liquid in a graduated cylinder and remove 7.0 mL. What volume remains?
A: 43.0 – 7.0 = 36.0 mL.
Q: Which element is the least electronegative: Li, Na, K, Fr?
A: Francium (Fr). It sits at the bottom of Group 1A, where electronegativity is lowest.
Significant figures and unit conversions are used in every quantitative topic in the course, from stoichiometry to gas laws to solution concentration. Density connects to states of matter and phase changes. Electronegativity ties directly into chemical bonding: the electronegativity difference between two atoms determines whether a bond is ionic, polar covalent, or nonpolar covalent, which is the foundation for molecular polarity and intermolecular forces.
significant figures, sig figs, leading zeros, trailing zeros, captive zeros, rounding, precision, accuracy, unit conversion, dimensional analysis, metres to centimetres, density, mass, volume, g/cm³, mL, graduated cylinder, meniscus, lab techniques, electronegativity, periodic trends, Pauling scale, bond polarity, francium, fluorine, CHEM 101, general chemistry