FLOOR

Returns a number rounded down to a multiple of another number.

Syntax:

FLOOR(number, mult, mode)

number is the number that is to be rounded down to a multiple of mult. If mode is zero or omitted, FLOOR rounds down to the multiple below (more negative than or equal to) number. If mode is non-zero, FLOOR rounds down towards zero. This difference is only relevant with negative numbers.Use mode=1 for compability if you have negative numbers.

Example:

FLOOR(8, 3)

returns 6, because 2*3 = 6 is the first multiple of 3 below 8.

FLOOR(6, 3)

returns 6.

FLOOR( -11, -2)

returns -12, rounding to the multiple below.

FLOOR( -11, -2, 0)

returns -12.

FLOOR( -11, -2, 1)

returns -10, because with mode=1 the function rounds towards zero.

Application:

Imagine you are a teacher, and you need to calculate the final grade for a group of students. The grading policy states that the final score is the average of three quizzes, and the final grade is the score rounded down to the nearest whole number. You can use the FLOOR function to achieve this.

Here's the data for four students:

	Student	Quiz 1 Score	Quiz 2 Score	Quiz 3 Score	Average Score	Final Grade (using FLOOR)
	A	B	C	D	E	F
1	Alice	85	92	88	88.333333333	88
2	Bob	78	85	80	81	81
3	Charlie	90	95	93	92.666666667	92
4	Dana	65	70	68	67.666666667	67

In this example, the "Average Score" is calculated by summing the three quiz scores and dividing by 3. The "Final Grade" is then determined by applying the FLOOR function to the "Average Score."

For instance, for Alice, the average score is (85+92+88)/3=88.33. The FLOOR function, applied to 88.33, returns 88. This is because the FLOOR function finds the greatest integer less than or equal to the input value. So, even though Alice's average is closer to 88 than to 89, the FLOOR function will always round down, ensuring that the final grade is a whole number that doesn't exceed her average score.