Certainly! Let's break down the problem step-by-step to find the lower and upper bounds for the length of the piece of string, which is rounded to the nearest centimeter.
### Step-by-Step Solution
The given length of the piece of string is 9 cm when rounded to the nearest centimeter. This indicates that the true length of the string could be slightly less than or slightly more than 9 cm, but within a certain range.
a) Lower Bound:
When we say a measurement is rounded to the nearest whole number, it implies that any value within 0.5 cm below or above the given number, when rounded, will result in that number.
Since the length provided is 9 cm, the smallest possible length that would round up to 9 cm would be just above 8.5 cm. Therefore, it makes sense to establish that:
[tex]\[ \text{Lower Bound} = 9 - 0.5 = 8.5 \text{ cm} \][/tex]
So, the lower bound of the length of the piece of string is 8.5 cm.
b) Upper Bound:
Similarly, the largest possible length that would round down to 9 cm would be just below 9.5 cm. Thus, the upper bound of the length can be determined as:
[tex]\[ \text{Upper Bound} = 9 + 0.5 = 9.5 \text{ cm} \][/tex]
So, the upper bound of the length of the piece of string is 9.5 cm.
### Summary
- a) The lower bound of the length of the piece of string is 8.5 cm.
- b) The upper bound of the length of the piece of string is 9.5 cm.
These bounds ensure that any length within this range would round to 9 cm when rounded to the nearest whole number.
