Unit 2: Measurements in Chemistry - Numbers in Chemistry Notes

The Anatomy of a Measurement

  • Every single measurement in chemistry consists of three essential parts. If any of these are missing, the measurement is incomplete or potentially meaningless:

    1. Number: The quantitative value expressed.
    2. Unit: The scale or standard of measurement (e.g., centimeters, liters, pounds).
    3. Significant Figures: The digits that convey the precision of the measurement.

  • Examples of measurement structure:

    • 55.6 cm55.6\,\text{cm}: This measurement contains 33 significant figures.
    • 5 cc5\,\text{cc}: This measurement contains 11 significant figure.
    • 30. nL30.\,\text{nL}: This measurement contains 22 significant figures (the decimal point after the zero indicates the zero is significant).

Classification of Numbers in Chemistry

  • Numbers in chemistry are categorized into two distinct types: Exact and Inexact.

  • Exact Numbers

    • Definition: These are numbers that result from counting objects specifically or are part of a defined value.
    • Uncertainty: These numbers contain no uncertainty.
    • Examples:
      • Counting objects: 5454 people, 1212 stitches, 55 puppies, 1212 garlic cloves, 33 apples.
      • Definitions/Groupings: 44 dozen (where a dozen is defined as exactly 12).

  • Inexact Numbers

    • Definition: These numbers result from any measurement or observation made with an instrument or tool.
    • Uncertainty: These numbers always contain some degree of uncertainty.
    • Source of Uncertainty: The level of uncertainty is determined by the smallest measured unit on the device used to take the measurement.
    • Examples:
      • 5 cm5\,\text{cm}
      • 10.5 lb10.5\,\text{lb}
      • 10 lb10\,\text{lb} (in the context of the combined weight of puppies)
      • 3 tsp3\,\text{tsp} (teaspoons of chopped onion used in a recipe)
      • 3.21 grams3.21\,\text{grams}
      • 100 miles100\,\text{miles}
      • 300.1 liters300.1\,\text{liters}

Knowledge Check #3.1: Identifying Number Types

  • Question: Identify each of the following numbers as an exact number or an inexact number.

  • Assessment and Key:

    • 3.21 grams3.21\,\text{grams}: Inexact (This is a measured mass).
    • 33 apples: Exact (These are counted whole objects).
    • 100 miles100\,\text{miles}: Inexact (This is a measured distance).
    • 300.1 liters300.1\,\text{liters}: Inexact (This is a measured volume).
    • 4 dozen4\,\text{dozen}: Exact (This is a defined quantity/count).