How do logarithms convert numbers like 8.7 and -2.3 to whole numbers?

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Discussion Overview

The discussion revolves around the mathematical concepts of rounding numbers using floor and ceiling functions, specifically how the numbers 8.7 and -2.3 are converted to whole numbers.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how 8.7 is converted to 8 and -2.3 to 2.
  • Another participant clarifies that 8.7 is not changed to 8 directly, but rather \lfloor8.7\rfloor is used, indicating the floor function rounds down to 8.
  • A different participant notes that \lceil -2.3 \rceil rounds up to -2, referencing the ceiling function.
  • A later reply acknowledges the use of ceiling and floor functions, indicating a misunderstanding of the notation as mere brackets.

Areas of Agreement / Disagreement

Participants appear to agree on the definitions and functions of ceiling and floor, but initial confusion exists regarding their notation and application.

Contextual Notes

Some participants may not have been familiar with the notation for ceiling and floor functions, leading to initial misunderstandings.

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5fdsQ.png


I am unsure of how they were able to change 8.7 to 8 and make -2.3 to 2. Whats the explanation behind this?
 
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mohabitar said:
5fdsQ.png


I am unsure of how they were able to change 8.7 to 8 and make -2.3 to 2. Whats the explanation behind this?

It's not that 8.7 was changed to 8, but that [tex]\lfloor8.7\rfloor[/tex] was changed to 8,since 8.7 rounded down is 8.
 
And [tex]\lceil -2.3 \rceil[/tex] is rounded up to -2.
 
Ohhhh I didnt even notice those were the ceiling and floor functions, I thought they were just brackets! Thanks!
 

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