A number 𝑦, when rounded to 1 decimal place, is equal to 0.4Find the upper and lower bound of 𝑦.

1. Break Down the Problem

To find the upper and lower bounds for the number $y$ 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

1. 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: $\text{Lower Bound} = 0.35$

2. 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: $\text{Upper Bound} = 0.45$

4. Verify and Summarize

To ensure accuracy:

• Numbers in the interval $[0.35, 0.45)$ 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 $y$ is $0.35$ and the upper bound is $0.45$. Thus, $y \in [0.35, 0.45)$