A weight is given as 3 kg (to the nearest kg). What is the lowest possible value of the actual weight?
Answer (2)
The weight is given as 3 kg to the nearest kg.
The actual weight, w , satisfies 2.5 ≤ w < 3.5 .
The lowest possible value of the actual weight is 2.5 kg.
The lowest possible value of the actual weight is 2.5 kg .
Explanation
Understanding the Problem When a weight is given as 3 kg to the nearest kg, it means that the actual weight, w , when rounded to the nearest whole number, is 3 kg. This implies that the actual weight lies within a certain range.
Determining the Range To find the lowest possible value of the actual weight, we need to determine the lower bound of this range. Since the weight is rounded to the nearest kg, the range is defined as:
2.5 ≤ w < 3.5
Identifying the Lowest Possible Value The lowest possible value of the actual weight is the lower bound of this range, which is 2.5 kg.
Final Answer Therefore, the lowest possible value of the actual weight is 2.5 kg.
Examples
In manufacturing, if a component is specified to weigh 3 kg to the nearest kg, it's crucial to know the minimum acceptable weight to ensure product quality. Knowing that the lowest possible actual weight is 2.5 kg helps in setting quality control standards and tolerances. For example, if the component weighs less than 2.5 kg, it might not meet the required strength or performance criteria, leading to rejection or rework.
The lowest possible value of the actual weight when rounded to 3 kg is 2.5 kg. This is derived from the range established by the rounding rules. Therefore, 2.5 kg ≤ w < 3.5 kg .
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