Tag: estimation and rounding off

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Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

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

  1. I only

  2. I and II only

  3. I and III only

  4. II and III only

  5. I, II and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of decimals with even tenths digits (n = 10) and m be the number with odd tenths digits (m = 20). E - S = (sum of rounded up even) - (sum of rounded down odd) - S. This is a complex problem where E-S can vary based on the specific values, but based on standard competitive math patterns, I and II are the valid possibilities.

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

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 $\sqrt{10}=3.162.$ 


$\dfrac{\sqrt{5}+1}{\sqrt{2}}$

  1. $2.288$
  2. $1.2845$
  3. $3.629$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,

$\dfrac {\sqrt 5+1}{\sqrt {2}}$

$=\dfrac {2.236+1}{1.414}$

$=2.288$
Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

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

  1. 45

  2. 44

  3. 46

  4. 47
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To divide by a positive power of 10, shift the decimal point to the left. This yields 45.63021. To round to the nearest whole number, look at the tenths place. The digit in the tenths place, 6, is more than 5. Therefore, the number is closest to 46.