A number 𝑦, when rounded to 1 decimal place, is equal to 0.4Find the upper and lower bound of 𝑦.
Question
A number 𝑦, when rounded to 1 decimal place, is equal to 0.4.
Find the upper and lower bound of 𝑦.
Solution
1. Break Down the Problem
To find the upper and lower bounds for the number when rounded to one decimal place, we need to understand how rounding works at this level of precision.
2. Relevant Concepts
When a number is rounded to one decimal place, it can take values that are in the range of:
- Lower Bound: The smallest number that rounds up to 0.4
- Upper Bound: The smallest number that rounds up to 0.5
3. Analysis and Detail
-
Lower Bound: The smallest number that rounds to 0.4 is 0.35. Any number below 0.35 will round down to 0.3. Hence, the lower bound is:
-
Upper Bound: The smallest number that still rounds to 0.5 is 0.45. Thus, any number up to (but not including) 0.45 will round to 0.4. Therefore, the upper bound is:
4. Verify and Summarize
To ensure accuracy:
- Numbers in the interval will round to 0.4.
- Numbers below 0.35 round to 0.3, and numbers 0.45 and above round to 0.5.
Final Answer
The lower bound of is and the upper bound is . Thus,
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