Tag: multiplication and division of decimals

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

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?

  1. 7

  2. 4

  3. 6

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $0.4$
  2. $0.04$
  3. $0.004$
  4. $0.0004$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given,

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


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

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

$= ( 0.768 - 0.568 )^2$

$= ( 0.2 )^2$

$= 0.04.$

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


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

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

  1. $0.1$
  2. $0.01$
  3. $1$
  4. $0.1 \times 0.1$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation
$0.3 \times 0.3 - 2\times 0.3 \times 0.2 + 0.2 \times 0.2$

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

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

$= ( 0.3 - 0.2 )^2$

$= ( 0.1)^2$

$= 0.1\times0.1$

$= 0.01.$

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