Tag: decimal fractions

Questions Related to decimal fractions

If $a, b, c$ are distinct $+ve$ real numbers and ${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=1$ then $ab + bc + ca$ is 

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

  1. less then $1$

  2. equal to $1$

  3. greater then $1$

  4. any real no.

Show answer
Correct Option: A
Explanation:

${a}^{2} + {b}^{2} + {c}^{2} = 1 \quad \left( \text{Given} \right)$


${\left( a +  b + c \right)}^{2} > 0$

${a}^{2} + {b}^{2} + {c}^{2} + 2 \left( ab + bc + ca \right) > 0$

$1 + 2 \left( ab + bc + ca \right) > 0$

$2 \left( ab + bc + ca \right) > -1$

$\Rightarrow ab + bc + ca >-\dfrac 12$

If the decimal o.d25d25d25 ................ is expressible in the form n/27, then d+n must be

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

  1. 9

  2. 28

  3. 30

  4. 34

Show answer
Correct Option: D
Explanation:

$x = 0.d25 d25d25 -----$
$x = 0.\overline{d25}$
$1000 x = d25. \overline{d25}$
$999 x = d 25$
$x = \displaystyle \frac{d 25}{999}$
$x = \displaystyle \frac{d25}{37.27}$
take d = 9 then $x = \displaystyle \frac{25}{27}$
$d = 9          n = 25$
$d + n = 34$

Express $ \dfrac {5}{13} $ correct to $3$ significant figures.

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

  1. $1.26$

  2. $0.385$

  3. $0.00385$

  4. $0.103$

Show answer
Correct Option: B
Explanation:

$\dfrac {5}{13} = 0.3846$


Rounding off to $3$ places to nearest decimal, we get $0.385$.
So, option $B$ is correct.

A $3$ digit id a $3$ digit number (not starting with zero) which reads the same backwards as forwards. For example $171$. The sum of all even $3$ digit palindromes, is 

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

  1. $22380$

  2. $25700$

  3. $22000$

  4. $22400$

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Correct Option: A

The number of significant digits in the measurement of the side of a square whose computed area is $1.1025$ square inches to the nearest tenthousandth of a square cm is

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

  1. $2$

  2. $3$

  3. $4$

  4. $5$

  5. $1$

Show answer
Correct Option: D
Explanation:

(d) is the correct choice.

Which of the following statements is incorrect regarding significant figures?

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

  1. All the non-zero digits are significant.

  2. All the zeros between two non-zero digits are significant.

  3. Greater the number of significant figures in a measurement, smaller is the percentage error.

  4. The power of 10 is counted while counting the number of significant figures.

Show answer
Correct Option: D
Explanation:

The term significant figures are referring to the number of important digits (0 through 9 inclusive) in the coefficient of some expression in the scientific notation. The number of significant figures in any expression indicate the confidence or precision with which we can state a quantity.

Some rules for significant figures are:

1. All non-zero numbers are significant.

2. Zeros located between non-zero digits are significant.

3. Trailing zeros at the end will be significant only if the number contains a decimal point; otherwise, they are insignificant.

4. Zeros to the left of the first nonzero digit are insignificant.

5. Number in exponents (for example power of 10) is insignificant.

Thus option D is correct. 

Divide $0.3297$ by $0.07$, correct to $2$ significant digits.

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. $4.4$

  2. $4.7$

  3. $4.9$

  4. None of these

Show answer
Correct Option: B
Explanation:

$0.3297 \div 0.07 = 4.71$

as the digit in ten's place is not greater than 5, it cannot be replaced.
$\therefore 0.3297 \div 0.07 = 4.7$

In the decimal, $2.4d7$, $d$ represents a digit from 0 to 9. If the value of the decimal rounded to the nearest tenth, is less than $2.5$, what are the possible values of $d$?

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. $0,1,2$

  2. $0,1,2,3,4$

  3. $5,6,7$

  4. $5,6,7,8,9$

Show answer
Correct Option: B
Explanation:

The correct answer is ${0,1,2,3,4}$.

: If $d \ge 5$, the decimal rounded to the nearest tenth will be greater than $2.5$.
Hence, option B is correct.

$\displaystyle 6.743\times 100$ is equal to _____ 

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. $674.300$

  2. $.674300$

  3. $67.4300$

  4. $6.74300$

Show answer
Correct Option: A
Explanation:

The number of decimal places from the right of the number in the question will be in the product at the same number of places.

$6.743×100=674.300$   ($3$ decimal places)
So option A is the correct answer.

Calculate the value of the following expression by appropriate rounding off of the numbers:
$\displaystyle 0.43\times 0.87=$

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. $0.31$

  2. $0.35$

  3. $0.36$

  4. $0.38$

Show answer
Correct Option: C
Explanation:
Since in the case of $0.43$, the last digit is less than $5$, it would be rounded off to $0.4$
Likewise, since the last digit of $0.87$ is greater than $5$, it would be rounded off to $0.9$
$0.43 \times 0.87$ thus becomes $0.4 \times 0.9 = 0.36$