Tag: calculations and mental strategies 4

Questions Related to calculations and mental strategies 4

If k is an integer, and if $0.02468 \times 10^k$ is greater than 10,000, what is the least possible value of k?

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. 7

  2. 4

  3. 6

  4. 5

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Correct Option: C
Explanation:

Multiplying 0.02468 by a positive power of 10 will shift the decimal point to the right. Simply shift the decimal point to the right until the result is greater than 10,000. Keep track of how many times you shift the decimal point. Shifting the decimal point 5 times results in 2,468. This is still less than 10,000. Shifting one more place yields 24,680, which is greater than 10,000.

The value of $0.768 \times 0.768 - 2 \times 0.768 \times 0.568 + 0.568 \times 0.568$ is:

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $0.4$

  2. $0.04$

  3. $0.004$

  4. $0.0004$

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Correct Option: B
Explanation:
Given,

$0.768 \times 0.768 - 2\times 0.768 \times 0.568 + 0.568 \times 0.568$


$= ( 0.768 )^2 - 2 \times  0.768 \times 0.568 + ( 0.568 )^2$

$Using\  identity \ \because { a^2 - 2 ab + b^2 = ( a - b )^2 }$

$= ( 0.768 - 0.568 )^2$

$= ( 0.2 )^2$

$= 0.04.$

$\therefore The\  option\ B\  is \ correct .$


The value of $\left( {0.3} \right)\left( {0.3} \right) - 2\left( {0.3} \right)\left( {0.2} \right) + \left( {0.2} \right)\left( {0.2} \right)$

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $0.1$

  2. $0.01$

  3. $1$

  4. $0.1 \times 0.1$

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Correct Option: B,D
Explanation:
$0.3 \times 0.3 - 2\times 0.3 \times 0.2 + 0.2 \times 0.2$

$= ( 0.3 )^2 - 2 \times  0.3 \times 0.2 + ( 0.2 )^2$

$Using\  identity \ \because { a^2 - 2 ab + b^2 = ( a - b )^2 }$

$= ( 0.3 - 0.2 )^2$

$= ( 0.1)^2$

$= 0.1\times0.1$

$= 0.01.$

$\therefore The\  option\ B\ and\ D\ both \ are\  \ correct .$

$\dfrac { 5\times 1.6-2\times 1.4 }{ 1.3 } =$?

maths calculations and mental strategies 4 written methods dividing decimals division of decimals

  1. $0.4$

  2. $1.2$

  3. $1.4$

  4. $4$

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Correct Option: D
Explanation:

Given Expression $=\dfrac { 8-2.8 }{ 1.3 } =\dfrac { 5.2 }{ 1.3 } =\dfrac { 52 }{ 13 } =4$

$\dfrac { 0.0203\times 2.92 }{ 0.0073\times 14.5\times 0.7 } =$?

maths calculations and mental strategies 4 written methods dividing decimals division of decimals

  1. $0.8$

  2. $1.45$

  3. $2.40$

  4. $3.25$

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Correct Option: A
Explanation:

$\dfrac { 0.0203\times 2.92 }{ 0.0073\times 14.5\times 0.7 } =\dfrac { 203\times 292 }{ 73\times 145\times 7 } =\dfrac { 4 }{ 5 } =0.8$