cs221 ยป

CS221 Floor

The notation \lfloor x \rfloor is used to denote the floor of x. The floor of x is the largest integer which is less than or equal to x. For example,

  1. \lfloor 3.4 \rfloor = 3
  2. \lfloor 3.8 \rfloor = 3
  3. \lfloor 3 \rfloor = 3
  4. \lfloor -3.4 \rfloor = -4
  5. \lfloor -3.8 \rfloor = -4

Exercises

Fill in the blanks.

  1. \lfloor 12.7234 \rfloor = ___
  2. \lfloor 12.12 \rfloor = ___
  3. \lfloor -12.7234 \rfloor = ___
  4. \lfloor -12.12 \rfloor = ___
  5. \lfloor \frac{12}{2} \rfloor = ___
  6. \lfloor \frac{13}{2} \rfloor = ___
  7. \lfloor \frac{14}{2} \rfloor = ___
  8. \lfloor \frac{15}{2} \rfloor = ___

Answers

  1. \lfloor 12.7234 \rfloor = 12
  2. \lfloor 12.12 \rfloor = 12
  3. \lfloor -12.7234 \rfloor = -13
  4. \lfloor -12.12 \rfloor = -13
  5. \lfloor \frac{12}{2} \rfloor = 6
  6. \lfloor \frac{13}{2} \rfloor = 6
  7. \lfloor \frac{14}{2} \rfloor = 7
  8. \lfloor \frac{15}{2} \rfloor = 7