Which statement explains why the value of [2.4] is 2 but the value of [-2.4] is –3?

because 2 is the greatest integer not greater than 2.4 and –3 is the greatest integer not greater than –2.4.

because 2.4 rounds to 2, and –2.4 rounds to –3.

because 2.4 is positive and –2.4 is negative, they are rounded in different ways.

because 2.4 and –2.4 are both divisible by 2 and by 3, the value of each expression can be ±2 or ±3.

For any x in Real numbers, [x] is the greatest possible integer smaller than x, or equal to x if x is an integer.

According to this,

[2.4] is the greatest integer , smaller than or equal to (so non greater) 2.4. This number is 2

similarly,  [-2.4] is the greatest integer , smaller than or equal to (so non greater) -2.4. This number is -3.

 

A) Because 2 is the greatest integer not greater than 2.4 and –3 is the greatest integer not greater than –2.4.