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

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4128
GPA: 3.39
A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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Updated on: 10 Feb 2019, 05:49
2
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:50) correct 48% (02:00) wrong based on 46 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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Last edited by SajjadAhmad on 10 Feb 2019, 05:49, 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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Updated on: 14 Feb 2019, 08:30
1
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..

Originally posted by Archit3110 on 10 Feb 2019, 05:45.
Last edited by Archit3110 on 14 Feb 2019, 08:30, edited 1 time in total.
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Joined: 12 Sep 2017
Posts: 302
A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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14 Feb 2019, 07:18
Archit3110 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

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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WE: Marketing (Telecommunications)
A bar below a digit in a decimal indicates an infinitely repeating dec  [#permalink]

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17 Feb 2019, 00:20
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] 17 Feb 2019, 00:20
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