The weight of a dog has been truncated to 402.3 ounces to 1dp. Work out the interval within which w, the weight of the dog, lies.

The weight of a dog has been rounded to 402.3 ounces, with one decimal place of precision. To determine the range in which the actual weight, denoted as w, falls, it is essential to consider the implications of rounding. When a number is rounded to one decimal place, it indicates that the true value could be as low as 402.25 ounces and as high as 402.35 ounces. This range accounts for the rounding process, ensuring that the actual weight is accurately represented.

To further elaborate, the lower limit of the interval is derived by subtracting 0.05 ounces from the rounded figure, resulting in 402.25 ounces. Conversely, the upper limit is established by adding 0.05 ounces to the rounded weight, yielding 402.35 ounces. Therefore, the weight of the dog, w, is confined within the interval of 402.25 ounces to 402.35 ounces. This method of determining the interval is a fundamental concept often revisited in GCSE Maths May Revision, emphasising the importance of understanding rounding in mathematical contexts.

In summary, the weight of the dog, when rounded to one decimal place as 402.3 ounces, suggests that the actual weight lies within a specific range. This range, from 402.25 ounces to 402.35 ounces, illustrates the precision involved in rounding and the significance of recognising the potential variations in measurements. Such calculations are crucial for students to master, as they form the basis for more complex mathematical concepts encountered in their studies.