Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Sure! Let's solve the problem step-by-step.
Given that the number [tex]\( x \)[/tex] has been truncated to a whole number and the result is 16, the truncation implies removing the decimal part without rounding. This means the number [tex]\( x \)[/tex] is between 16 and just under 17.
### Step-by-Step Solution:
1. Understanding Truncation:
- When we truncate a number to the whole number 16, this implies that [tex]\( x \)[/tex] is at least 16 because truncating any number between 16 (inclusive) and 17 (exclusive) results in 16.
2. Defining the Interval:
- Therefore, the lower bound of [tex]\( x \)[/tex] is 16.
- The upper bound of [tex]\( x \)[/tex] is just less than 17, since if [tex]\( x \)[/tex] were 17 or more, its truncated whole number would be 17, not 16.
3. Expressing the Error Interval:
- Combining these bounds together, the interval can be written as:
[tex]\[ 16 \leq x < 17 \][/tex]
Thus, the error interval for [tex]\( x \)[/tex] is:
[tex]\[ 16 \leq x < 17 \][/tex]
This properly captures the set of all numbers that would truncate to 16 when the decimal portion is removed.
Given that the number [tex]\( x \)[/tex] has been truncated to a whole number and the result is 16, the truncation implies removing the decimal part without rounding. This means the number [tex]\( x \)[/tex] is between 16 and just under 17.
### Step-by-Step Solution:
1. Understanding Truncation:
- When we truncate a number to the whole number 16, this implies that [tex]\( x \)[/tex] is at least 16 because truncating any number between 16 (inclusive) and 17 (exclusive) results in 16.
2. Defining the Interval:
- Therefore, the lower bound of [tex]\( x \)[/tex] is 16.
- The upper bound of [tex]\( x \)[/tex] is just less than 17, since if [tex]\( x \)[/tex] were 17 or more, its truncated whole number would be 17, not 16.
3. Expressing the Error Interval:
- Combining these bounds together, the interval can be written as:
[tex]\[ 16 \leq x < 17 \][/tex]
Thus, the error interval for [tex]\( x \)[/tex] is:
[tex]\[ 16 \leq x < 17 \][/tex]
This properly captures the set of all numbers that would truncate to 16 when the decimal portion is removed.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.