Tag: estimation and rounding off

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Questions Related to estimation and rounding off

Multiple choice maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

Rohit's teacher asked him to tell the correct answer after performing the steps given.
$\bullet$ Round off $43, 98$ and $250$ to nearest tens.
$\bullet$ After rounding off, add them.
$\bullet$ Round off the sum to the nearest hundreds.
Then, the correct answer is __________.

  1. $300$
  2. $400$
  3. $350$
  4. $480$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rounding off to nearest tens:

If unit digit is $0,1,2,3,4$ then round down to nearest tens.
If unit digit is $5,6,7,8,9$ then, round up to nearest tens.
$43$ $\rightarrow$ $40$
$98$ $\rightarrow$ $100$
$250$ $\rightarrow$ $250$
$40+100+250$ $\rightarrow$ $390$
$390$  $\rightarrow$  $400$
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

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 $0.4 \times 0.9 = 0.36$
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

While rounding off, if the digit to be dropped is less than $5$, then the preceding digit:

  1. increases by $1$

  2. remains unchanged
  3. decreases by $1$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
When rounding, you examine the digit following (i.e., to the right of) the digit that is to be the last digit in the rounded off number. The digit you are examining is the first digit to be dropped.

  1. If that first digit to be dropped is less than $5$ (that is, $1, 2, 3 $ or $4$), drop it, and also drop all the digits to the right of it.
  2. If that first digit to be dropped is more than $5$ (that is, $6, 7, 8$ or $9$), increase by 1 the number to be rounded, that is, the preceeding digit (to the digit being dropped).
Thus, in our case, since the digit to be dropped is less than $5$, we make no change to the preceding digit. 
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

Sohan wishes to order salt for himself, but the salt is only sold in $30$-pound bags. He currently has $75$ pounds of salt, and he needs to have a minimum of $200$ pounds. Determine the inequality which shows the possible values for the number of bags, b, that Macro needs to order in order to meet his minimum requirement.

  1. $\displaystyle b\ge 4$
  2. $\displaystyle b\ge 5$
  3. $\displaystyle b\ge 6$
  4. $\displaystyle b\ge 7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sohan needs to have $200$ pounds but he currently has $75$ pounds

And bags sold only $30$ pounds bag.
Then sohan take bags in $75$ pounds $=$ $\dfrac{75}{30}=2.5$ says 2
But he needed bages in $200$ pounds $=$ $\dfrac{200}{30}=6.67$ says 7
Then the inequality of number of bags (b) $=6.67-2.5=4.16$ says $5$
Hence, option B is correct.