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A bar below a digit in a decimal indicates an infinitely repeating dec

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A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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New post Updated on: 10 Feb 2019, 04:49
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A
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Difficulty:

  45% (medium)

Question Stats:

61% (01:56) correct 39% (01:58) wrong based on 23 sessions

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A bar below a digit in a decimal indicates an infinitely repeating decimal. 333,333.3 × \((10^{–3} – 10^{–5})\) =

A. 3,333.3
B. 3,330
C. 333.3
D. 330
E. 0

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Originally posted by SajjadAhmad on 10 Feb 2019, 04:23.
Last edited by SajjadAhmad on 10 Feb 2019, 04:49, edited 2 times in total.
Edited the question.
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A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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New post Updated on: 14 Feb 2019, 07:30
1
SajjadAhmad wrote:
A bar below a digit in a decimal indicates an infinitely repeating decimal. 333,333.3 × \((10^{–3} – 10^{–5})\) =

A. 3,333.3
B. 3,330
C. 333.3
D. 330
E. 0


jfranciscocuencag
solution as follows
lets solve question in two parts

given
333,333.3 × \((10^{–3} – 10^{–5})\)

first solve for 10^-3 - 10^-5

10^-3-10^-5 ;
10^-3( 1-10^-2)
10^-3 ( 100-1/100)
10^-3 * ( .99)
or say 9.9*10^-4

now we have
333333.33 * 9.9*10^-4

9.9~ 10 ; 9.9 * 10^-4 = 10^-3

333333.33* 10 ^-3
=> will give us 333.333
since 10>9 ; so our answer would be little low than 333.333 i.e 330

hope this helps..
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Originally posted by Archit3110 on 10 Feb 2019, 04:45.
Last edited by Archit3110 on 14 Feb 2019, 07:30, edited 1 time in total.
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A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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New post 14 Feb 2019, 06:18
Archit3110 wrote:
SajjadAhmad wrote:
A bar below a digit in a decimal indicates an infinitely repeating decimal. 333,333.3 × \((10^{–3} – 10^{–5})\) =

A. 3,333.3
B. 3,330
C. 333.3
D. 330
E. 0



m](10^{–3} – 10^{–5})[/m] = 9.9*1-^-4

so
333,333.3 ×9.9*1-^-4
= 330
IMO D


Hello Archit3110 SajjadAhmad !

Could you please provide a detailed explanation?

I don't know what to do after this:

\((10^{–3} – 10^{–5})\)

\(10^{–3}(1 – 10^{–2})\)

\(99/10^{5}\)

So

333,333.3 = \(3/9\) = \(1/3\)

\(333,333.(1/3)(99/10^{5})\) ... Recurring terminal

\(333,333.(33/10^{5})\)

\(333,333.(33*10^{-5})\) ... after this I dont know that do do =/.

Kind regards!
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A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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New post 16 Feb 2019, 23:20
SajjadAhmad wrote:
A bar below a digit in a decimal indicates an infinitely repeating decimal. 333,333.3 × \((10^{–3} – 10^{–5})\) =

A. 3,333.3
B. 3,330
C. 333.3
D. 330
E. 0


Let's break the equation into two parts:

For --> 333,333.3
Multiply numerator and denominator by 3:
(333,333.3 × 3)/3 = 1000000/3 = \((10^{6})\) / 3

For --> \((10^{–3} – 10^{–5})\)
We can rewrite it to below:
\(((10^{-5}) * (10^{2} - 1)\)
= (100 - 1)/\((10^{5})\) = 99 / \((10^{5})\)

Now lets combine the two we get:

\(({10^{6}} * 99)/ (3 * {10^{-5}})\) = 33 * 10 = 330

Hence the correct answer is D.
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A bar below a digit in a decimal indicates an infinitely repeating dec   [#permalink] 16 Feb 2019, 23:20
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