Exact numbers

(noun)

These numbers are either defined numbers or result of a count. They have an infinite number of significant figures.

Examples of Exact numbers in the following topics:

  • Exact Numbers

    • Exact numbers are defined numbers or result from a count, unlike measured numbers.
    • Exact numbers are either defined numbers or the result of a count.
    • An exact number can only be expressed in one way and cannot be simplified any further.
    • Exact numbers have an infinite number of significant figures, but they often appear as integers.
    • Counted numbers are exact: there are two chairs in the photograph.

  • Molecular Formulas

    • Molecular formulas describe the exact number and type of atoms in a single molecule of a compound.
    • The empirical formula is the simplest whole number ratio of all the atoms in a molecule.
    • The molecular formula indicates the exact number of atoms in the molecule.
    • The empirical formula expresses the smallest whole number ratio of the atoms in the element.
    • Because of this, one molecular formula can describe a number of different chemical structures.

  • Polyatomic Molecules

    • For example, carbohydrates have the same ratio (carbon: hydrogen: oxygen = 1:2:1) and thus the same empirical formula, but have different total numbers of atoms in the molecule.
    • The molecular formula characterizes different molecules by reflecting their exact number of compositional atoms.

  • Molecules

    • Molecular size varies depending on the number of atoms that make up the molecule.
    • The full elemental composition of a molecule can be precisely represented by its molecular formula, which indicates the exact number of atoms that are in the molecule.

  • Writing Lewis Symbols for Atoms

    • Since we have established that the number of valence electrons determines the chemical reactivity of an element, the table orders the elements by number of valence electrons.
    • Furthermore, the number of columns (or groups) from the left edge of the table tells us the exact number of valence electrons for that element.
    • Some periodic tables list the group numbers in Arabic numbers instead of Roman numerals.
    • Lewis symbols for the elements depict the number of valence electrons as dots.
    • Electrons can inhabit a number of energy shells.

  • Avogadro's Number and the Mole

    • The mole is represented by Avogadro's number, which is 6.02×1023 mol-1.
    • Although he did not determine the exact proportion, he is credited for the idea.
    • Avogadro's number is defined as the number of elementary particles (molecules, atoms, compounds, etc.) per mole of a substance.
    • Avogadro's number is 6.022×1023 molecules.
    • With Avogadro's number, scientists can discuss and compare very large numbers, which is useful because substances in everyday quantities contain very large numbers of atoms and molecules.

  • Significant Figures

    • Significant figures of a number are digits which contribute to the precision of that number.
    • Numbers that do not contribute any precision and should not be counted as a significant number are:
    • For example, it may not always be clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty.
    • When multiplying and dividing numbers, the number of significant figures used is determined by the original number with the smallest amount of significant figures.
    • Start counting sig figs at the first non-zero number and continue to the end of the number.

  • Balancing Redox Equations

    • Balancing redox reactions depends on conservation of mass and electrons; the exact method varies with basic or acidic solutions.
    • Multiply the half-reactions by the appropriate number so that they have equal numbers of electrons.
    • This pair of half-reactions can be balanced by ensuring that both have the same number of electrons.
    • Multiply the half-reactions by the appropriate number so that they have equal numbers of electrons.
    • Step 4: Multiply the half-reactions by the appropriate number so that they have equal numbers of electrons.

  • Elemental Boron

    • Boron is a chemical element with the chemical symbol B and atomic number 5.
    • Natural boron is composed of two stable isotopes: 11B is more abundant than 10B, which has a number of uses as a neutron-capturing agent.
    • Boron is essential to life, although its exact physiological role in animals is not well-established.

  • Mass-to-Mole Conversions

    • Because scientists of the early 18th and 19th centuries could not determine the exact masses of the elements due to technology limitations, they instead assigned relative weights to each element.
    • This video describes how to determine the number of moles of reactants and products if given the number of grams of one of the substances in the chemical equation.