Final answer:
The original statement is false because not all the given reasons for rounding 2.4 to 2 and -2.4 to -3 are correct. They are rounded based on their value in relation to the nearest whole number, and divisibility by 2 or 3 is not directly relevant in this context. Additionally, rounding does not always result in ±2 or ±3.
Step-by-step explanation:
The question revolves around understanding how numbers are rounded, how signs affect multiplication and division, and significant figures. When rounding, numbers are typically rounded to the nearest integer. 2.4 is rounded down to 2, and -2.4 is rounded down to -3. However, both -2.4 and 2.4 are not divisible by 3 since the division would result in a non-integer. Only even numbers are divisible by 2, and while 2.4 can be divided by 2 giving 1.2, -2.4 can also be divided by 2 giving -1.2.
Whenever two positive numbers or two negative numbers multiply, the result has a positive (+ve) sign, but if they have opposite signs, the result has a negative (-ve) sign. The same rules apply to division. In addition and subtraction, the precision of the decimal place is determined by the term with the fewest decimal places.