Tag: estimations, bounds and rounding off

Choose the correct alternative.
If $\bar {d}=-20.83,\bar {x}=254.17$, then $A=?$

List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S.The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If $\displaystyle \frac { 1 }{ 3 } $ of the decimals in T have a tenths digit that is even, which of the following is a possible value of E- S ? 
I. -16
II. 6
III.10

Find the value to three places of decimal of  the following. It is given that $\sqrt{2}=1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236$ and $\sqrt{10}=3.162.$ 

What is $4,563,021 \div 10^5$, rounded to the nearest whole number?