Respuesta :
Answer:
The error interval for x is:
[3.65,3.74]
Step-by-step explanation:
The number after rounding off is obtained as:
3.7
We know that any of the number below on rounding off the number to the first decimal place will result in 3.7:
3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74
( Because if we have to round off a number present in decimals to n place then if there is a number greater than or equal to 5 at n+1 place then it will result to the one higher digit at nth place on rounding off and won't change the digit if it less than 5 )
Hence, the error interval is:
[3.65,3.74]
The error interval will be [3.65,3.75).
What is an error interval?
The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.
Given here the decimal number is 3.7 which is after rounded to 1 decimal place.
As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05
Then the lower limit of the error interval will be 3.7-0.05= 3.65
the higher limit of the error interval will be 3.7+0.05= 3.75
the error interval will be 3.65≤x<3.75
As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.
There are the numbers below which on rounding give 3.7
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
Therefore the error interval will be [3.65,3.75).
Learn more about error intervals
here: https://brainly.com/question/23923516
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