Difficulty: Introductory Prerequisites: None, though basic comfort with algebra helps.
This material covers the foundational toolkit you will use in every chemistry calculation for the rest of the course: knowing your elements by name and symbol, converting between units without error, expressing very large or very small numbers cleanly, and understanding how measurement precision works. If you are coming in cold, start here. Everything from stoichiometry to thermodynamics relies on these mechanics, and exams will test them both directly and as part of larger problems.
Memorize the first 20 elements (hydrogen through calcium) by symbol and name. Learn to convert between metric units using dimensional analysis (multiply by a conversion factor so unwanted units cancel). Express very large or very small numbers in scientific notation as C × 10ⁿ, where C is between 1 and 9.
Element
A pure substance made of only one type of atom, identified by its atomic number. Think of it as the simplest building block of all matter.
Chemical symbol
A one- or two-letter abbreviation for an element (e.g. Na for sodium, C for carbon). The first letter is always capitalised; the second, if present, is always lowercase.
Dimensional analysis (factor-label method)
A technique for converting between units by multiplying by conversion factors arranged so that unwanted units cancel. In simple terms, you set up fractions so the old unit divides out and the new unit remains.
Conversion factor
A fraction equal to 1, built from an equivalence between two units (e.g. 1 m / 100 cm or 100 cm / 1 m). You choose whichever form cancels the unit you want to get rid of.
Scientific notation
A way to write any number as C × 10ⁿ, where C (the coefficient) is between 1 and 9 and n (the exponent) is an integer. In simple terms, it lets you handle very large or very small numbers without writing out a string of zeros.
Coefficient (in scientific notation)
The number in front of the power of ten. It must be at least 1 and less than 10.
Exponent (in scientific notation)
The power of ten that tells you how many places to shift the decimal. Positive means a large number; negative means a small one.
You need to know these by heart: symbol to name and name to symbol.
# | Symbol | Name | # | Symbol | Name |
|---|---|---|---|---|---|
1 | H | Hydrogen | 11 | Na | Sodium |
2 | He | Helium | 12 | Mg | Magnesium |
3 | Li | Lithium | 13 | Al | Aluminum |
4 | Be | Beryllium | 14 | Si | Silicon |
5 | B | Boron | 15 | P | Phosphorus |
6 | C | Carbon | 16 | S | Sulfur |
7 | N | Nitrogen | 17 | Cl | Chlorine |
8 | O | Oxygen | 18 | Ar | Argon |
9 | F | Fluorine | 19 | K | Potassium |
10 | Ne | Neon | 20 | Ca | Calcium |
Pay special attention to symbols that do not match the English name: Na (sodium, from Latin natrium), K (potassium, from Latin kalium), and note that some symbols share a first letter (C = carbon, Ca = calcium, Cl = chlorine).
The idea is straightforward: multiply your starting value by one or more conversion factors so the units you want to remove cancel out.
Start with the given quantity and its unit.
Write a conversion factor as a fraction with the unit you want to cancel in the denominator.
The unit you want to end up with goes in the numerator.
Multiply straight through.
Example 1: Convert 1.25 g to mg.
Conversion factor: 1 g = 1000 mg
1.25 g × (1000 mg / 1 g) = 1250 mg
Example 2: Convert 544 mL to L.
Conversion factor: 1000 mL = 1 L
544 mL × (1 L / 1000 mL) = 0.544 L
Nursing note: 5 mL = 1 teaspoon is a conversion factor that comes up in dosage calculations.
Any number can be written as C × 10ⁿ.
C (the coefficient) must be at least 1 and less than 10 (one non-zero digit before the decimal point).
n (the exponent) is positive for numbers greater than 1, negative for numbers less than 1.
To convert a large number: move the decimal left until you have one digit before it. Count the places you moved; that count is n.
15,300 → 1.53 × 10⁴ (decimal moved 4 places left)
To convert a small number: move the decimal right. The count becomes a negative exponent.
0.0042 → 4.2 × 10⁻³ (decimal moved 3 places right)
Scientific notation format:
C × 10ⁿ, where 1 ≤ C < 10 and n is an integer.
Unit conversion setup:
Starting value × (desired unit / given unit) = answer in desired unit
Common metric conversion factors:
Equivalence | Conversion factors |
|---|---|
1 m = 100 cm | 100 cm / 1 m or 1 m / 100 cm |
1 g = 1000 mg | 1000 mg / 1 g or 1 g / 1000 mg |
1 L = 1000 mL | 1000 mL / 1 L or 1 L / 1000 mL |
1 kg = 1000 g | 1000 g / 1 kg or 1 kg / 1000 g |
5 mL = 1 tsp | 5 mL / 1 tsp or 1 tsp / 5 mL |
Dimensional analysis is the same method pharmacists and nurses use to calculate drug dosages: "the patient needs X mg, the vial contains Y mg/mL, so administer Z mL." Getting the conversion factor upside down is a genuine patient-safety issue, which is why this skill is drilled so heavily in introductory chemistry.
Scientific notation turns up constantly in science and engineering. Distances in astronomy (the Sun is about 1.5 × 10⁸ km from Earth) and sizes in biology (a typical bacterium is roughly 1 × 10⁻⁶ m) would be unmanageable without it.
Students often confuse the direction of a conversion. If you are going from grams to milligrams, you multiply by 1000 (the number gets larger, not smaller). A quick sense-check: milligrams are a smaller unit, so the numerical value must be bigger.
Some students think any number with a decimal point is in scientific notation. It is not. Scientific notation specifically requires the form C × 10ⁿ with 1 ≤ C < 10.
Writing 15.3 × 10³ is not proper scientific notation because 15.3 is not between 1 and 9. The correct form is 1.53 × 10⁴.
Students sometimes assume that element symbols are just the first two letters of the English name. Several symbols come from Latin names (Na, K, Fe, Ag, Au, and others you will meet later), so memorisation is necessary.
⚠️ The first 20 elements table is a straight memorisation target. Expect a quiz where you are given symbols and must supply names, or vice versa.
⚠️ Dimensional analysis problems will appear on nearly every exam, often embedded inside larger stoichiometry or solution-chemistry questions. If you cannot set up unit cancellations quickly, everything downstream slows down.
⚠️ Scientific notation is tested both as a standalone skill ("express 0.00032 in scientific notation") and as part of significant-figures problems.
True or false: The chemical symbol for potassium is P.
Fill in the blank: 2.5 L = ______ mL.
True or false: In scientific notation, 32.1 × 10² is written correctly.
Fill in the blank: The symbol Na stands for ______.
True or false: To convert milligrams to grams, you multiply by 1000.
Answers: 1. False (K). 2. 2500. 3. False (should be 3.21 × 10³). 4. Sodium. 5. False (you divide by 1000, i.e. multiply by 1/1000).
Q: What is the chemical symbol for calcium, and what is the name of the element with the symbol Cl?
A: Calcium is Ca. Cl is chlorine.
Q: Convert 0.75 kg to grams using dimensional analysis. Show the setup.
A: 0.75 kg × (1000 g / 1 kg) = 750 g. The kg units cancel, leaving grams.
Q: Express 0.00047 in proper scientific notation.
A: 4.7 × 10⁻⁴. Move the decimal 4 places to the right to get a coefficient between 1 and 10; the exponent is negative because the original number is less than 1.
Q: A patient needs 10 mL of liquid medication. How many teaspoons is that?
A: 10 mL × (1 tsp / 5 mL) = 2 teaspoons.
Q: Is 45 × 10² valid scientific notation? If not, correct it.
A: No. The coefficient must be between 1 and 10. The correct form is 4.5 × 10³.
The first 20 elements reappear constantly: in ionic and covalent bonding (Chapter 2+), in balancing chemical equations, and in naming compounds. Dimensional analysis is the backbone of stoichiometry, where you will chain multiple conversion factors together (moles to grams, grams to moles, moles to particles). Scientific notation feeds directly into significant figures, which is covered in the companion study notes for this lecture.
first 20 elements, periodic table basics, element symbols, metric conversions, unit conversion, factor-label method, dimensional analysis, scientific notation, coefficient, exponent, powers of ten, CHEM 111, general chemistry, Purdue, nursing dosage conversion, mL to L, g to mg, teaspoon to mL