Tag: non-terminating recurring decimals in rational numbers

Questions Related to non-terminating recurring decimals in rational numbers

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

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

  1. I only

  2. I and II only

  3. I and III only

  4. II and III only

  5. I, II and III

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Correct Option: B

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 $\sqrt{10}=3.162.$ 


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

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

  1. $2.288$

  2. $1.2845$

  3. $3.629$

  4. None of the above

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Correct Option: A
Explanation:
Given,

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

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

$=2.288$

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

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

  1. 45

  2. 44

  3. 46

  4. 47

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Correct Option: C
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.

Round off each of the following as required.

$5.5493$ correct to two decimal places.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals

  1. $5.00$

  2. $5.54$

  3. $5.50$

  4. $5.55$

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Correct Option: D
Explanation:

As the third digit is greater than $5$, the second digit $4$ can be rounded to $5$.
Thus, rounding off $5.5493$ gives $5.55$.

The correct expansion of $6.\overline {46}$ in the fractional form is :

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals

  1. $\dfrac{646}{99}$

  2. $\dfrac{640}{100}$

  3. $\dfrac{64640}{1000}$

  4. $\dfrac{640}{99}$

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Correct Option: D
Explanation:

$6.\overline {46} = 6+ \overline {46}= 6+\dfrac{46}{99}=\dfrac{594+46}{99}=\dfrac{640}{99}$

Multiply $4.28$ and $0.67.$ Round off the product obtained correct to three decimal places

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals

  1. $2.798$

  2. $2.868$

  3. $0.85$

  4. None of these

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Correct Option: B
Explanation:

$4.28 \times 0.67 = 2.8676$

As the digit in the fourth place $(6)$ is greater than $5,$ it will get rounded.
$\therefore  2.8676$  can be written as $2.868$, correct to three decimal places.