practice Give the boundaries of the given value 87.5 yards
The Correct Answer and Explanation is:
Boundaries of the Given Value: 87.5 Yards
- Lower Boundary: 87.45 yards
- Upper Boundary: 87.55 yards
Explanation
When we are asked to give the boundaries of a given value such as 87.5 yards, we typically refer to the upper and lower class boundaries or precision boundaries depending on the context. These boundaries define the smallest and largest possible values that the number could reasonably represent, based on the precision it is rounded to.
Understanding Place Value and Precision
The value 87.5 yards is given to one decimal place. This means it is rounded to the nearest tenth, or 0.1 yard. To determine the boundaries of this rounded value, we assume that any value from halfway below to halfway above would round to 87.5.
Step-by-step Boundary Calculation
- Identify the place value:
- 87.5 is to 1 decimal place, which is the tenths place (0.1).
- Half of the unit in the place value:
- Half of 0.1 = 0.05
- Subtract and add this to the given value:
- Lower boundary = 87.5 − 0.05 = 87.45 yards
- Upper boundary = 87.5 + 0.05 = 87.55 yards
Therefore, any value from 87.45 up to but not including 87.55 would round to 87.5 if rounded to 1 decimal place. This is how we define the class boundaries or interval limits of 87.5.
Why This Matters
This concept is important in fields like statistics, measurement, and science, where precise interpretation of numerical data is required. Understanding boundaries helps to avoid errors due to rounding and ensures accurate data grouping in frequency tables, histograms, or data analysis.
In summary, the boundaries of 87.5 yards are 87.45 and 87.55, assuming it’s rounded to one decimal place.
