Tag: decimal fractions

Quizzes (26) Questions (52)

Questions Related to decimal fractions

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

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

  1. less then $1$
  2. equal to $1$
  3. greater then $1$

  4. any real no.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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


${\left( a +  b + c \right)}^{2} > 0$

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

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

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

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

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

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

  1. 9

  2. 28

  3. 30

  4. 34
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $x = \displaystyle \frac{25}{27}$
$d = 9          n = 25$
$d + n = 34$

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

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 

  1. $22380$
  2. $25700$
  3. $22000$
  4. $22400$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A 3-digit palindrome is of the form ABA. For it to be even, A must be 2, 4, 6, or 8. B can be 0-9. For each A, there are 10 possibilities for B. Summing these values: 202+212+...+292, 404+414+...+494, etc. The sum is 22380.

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

Which of the following statements is incorrect regarding significant figures?

  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.
Reveal answer Fill a bubble to check yourself
D Correct answer
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. 

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

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

  1. $4.4$
  2. $4.7$
  3. $4.9$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$0.3297 \div 0.07 = 4.71$

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

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

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 $d$?

  1. $0,1,2$
  2. $0,1,2,3,4$
  3. $5,6,7$
  4. $5,6,7,8,9$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $674.300$
  2. $.674300$
  3. $67.4300$
  4. $6.74300$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $0.31$
  2. $0.35$
  3. $0.36$
  4. $0.38$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $0.4 \times 0.9 = 0.36$