Discrete vs Continuous Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Discrete vs Continuous.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Discrete quantities come in separate, countable units; continuous quantities can take any value.

People come in whole numbers (discrete). Height can be any value (continuous).

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Discrete quantities come in separate countable steps; continuous quantities can take any value with no gaps between them.

Common stuck point: Digital measurements look continuous but are actually discrete (pixels, bits).

Sense of Study hint: Ask yourself: does it make sense to have 2.7 of this thing? If yes (like 2.7 kg), it is continuous. If no (like 2.7 people), it is discrete.

Worked Examples

Example 1

easy
Classify each quantity as discrete or continuous, and explain: (a) number of students in a class, (b) the height of a student, (c) the number of text messages sent, (d) the temperature in a room.

Solution

  1. 1
    (a) Number of students: must be a whole number (can't have 0.5 students). Discrete.
  2. 2
    (b) Height: can take any value in a range (e.g., 162.7 cm, 162.73 cm, etc.). Continuous.
  3. 3
    (c) Number of texts: whole numbers only. Discrete.
  4. 4
    (d) Temperature: can take any real value in a range (e.g., 20.1°, 20.15°, etc.). Continuous.

Answer

Discrete: (a) and (c); Continuous: (b) and (d).
Discrete quantities are counted (whole numbers, gaps between values), while continuous quantities are measured (any real value possible in an interval). The distinction matters for choosing the right mathematical model and type of graph.

Example 2

medium
A discrete model counts bacteria in a culture as B(t) = 2^t (where t is in hours, integer values). A continuous model uses B(t) = e^{0.693t}. Compare the models at t = 0, 1, 2, 3 and explain when each is appropriate.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Which type of graph is appropriate for each: (a) the number of cars sold each month (bar chart or line graph with any real y-values?), (b) the speed of a car over a journey?

Example 2

medium
Shoe sizes in the UK come in steps of \frac{1}{2} (e.g., 6, 6.5, 7, 7.5, \ldots). Is shoe size discrete or continuous? What about actual foot length in centimetres?
← Back to Discrete vs Continuous Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

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