Final answer:
Approximating numbers to a specified number of decimal places or significant figures involves rounding based on standard rules. Examples provided demonstrate rounding a decimal to five significant figures and determining confidence intervals based on statistics calculator outputs.
Step-by-step explanation:
To approximate the numbers 5 0.95 and 5 1.1, we would typically use rounding rules to round our answers to the desired number of decimal places or significant figures. The examples provided indicate calculations that have been rounded to a certain number of significant figures for clarity and precision in reporting statistical and measurement data.
The explanation about the calculator answer being 2,085.5688 but needing to be rounded to five significant figures demonstrates this process: Since the first digit to be dropped (in the tenths place) is greater than 5, we round up to 2,085.6.
Regarding the confidence interval calculation, after entering the values into a statistical calculator, the interval is given as (0.81003, 0.87397) which represents a 95 percent confidence that the true proportion of a statistic lies within this range.
Keep in mind, when rounding, that the presence of inexact numbers in a calculation dictates the precision of the answer. For example, with three inexact numbers in a calculation, the answer must be limited to the smallest number of significant figures among those inexact numbers.
Finally, for rounding numbers such as 0.0004505 and 5.00 x 10-6, these should be rounded to three significant figures, following the standard rules of rounding based on the value of the digit following the last significant figure.