Tag: calculating and mental strategies 3

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Questions Related to calculating and mental strategies 3

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of $\displaystyle \left( { 10 }^{ 4 }-{ 10 }^{ 2 } \right) \left( 0.00\overline { 12 }  \right) $

  1. 0
  2. $\displaystyle 0.\overline { 12 } $

  3. 1.2

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

$\displaystyle \left( { 10 }^{ 4 }-{ 10 }^{ 2 } \right) \left( 0.00\overline { 12 }  \right) $

= $ 9900 \times $ $0.00\overline{12}$
= $ 99 $ $\times$ $0.\overline{12}$..................(1)
Also, we know that
$ 0.\overline{12} $ = X
$ 12.\overline{12}$= 100X
Thus, 99X = 12 or X = $\cfrac{12}{99}$
So, (1) becomes
$99 \times \cfrac{12}{99} = 12$ So, option E

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

Which one of the following is a non-terminating and repeating decimal?

  1. $\dfrac {13}{8}$
  2. $\dfrac {3}{16}$
  3. $\dfrac {3}{11}$
  4. $\dfrac {137}{25}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Clear, $\dfrac {1}{8}=0.125, \dfrac {1}{16}=0.0625$ and $\dfrac {1}{25}=0.04$ are terminating decimal fractions.
So, $\dfrac {3}{11}=0.27272727....$ is the non-terminating and repeating decimal.