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

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Bunuel
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A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   07 Sep 2021, 04:00
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56% (02:12) correct 44% (02:13) wrong based on 181 sessions
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A bar above a digit in a decimal indicates an infinitely repeating decimal. \(333,333.\overline {3}*(10^{–3} – 10^{–5})\) =


A. \(3,333.\overline {3}\)

B. \(3,330\)

C. \(333.\overline {3}\)

D. \(330\)

E. \(0\)
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D
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yashikaaggarwal
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   15 Sep 2021, 10:20
Simply solve bracket.
(10^-3-10^-5)
= (99/100,000)
Now,
=> 333,333.33*99/100,000
=> 333.33*99
Which is surely slightly less than 333.33
Hence
D is the approximate answer.

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BrentGMATPrepNow
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   15 Sep 2021, 13:04
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Bunuel wrote:
A bar above a digit in a decimal indicates an infinitely repeating decimal. \(333,333.\overline {3}*(10^{–3} – 10^{–5})\) =


A. \(3,333.\overline {3}\)

B. \(3,330\)

C. \(333.\overline {3}\)

D. \(330\)

E. \(0\)


Key properties:
Multiplying number K by \(10^n\) (where n is positive) moves the decimal place to the RIGHT n spaces.
Multiplying number K by \(10^{-n}\) (where n is positive) moves the decimal place to the LEFT n spaces.

Some examples:
\(1234.567 * 10^{-2} = 12.34567\)
\(123456.7 * 10^{-5} = 1.234567\)
\(8,888,888.\overline {8} * 10^{-4} = 888.\overline {8}\)

Now onto the question!!

We get: \(333,333.\overline {3}*(10^{–3} – 10^{–5}) = 333.\overline {3} - 3.\overline {3}=330\)

Answer: D
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   23 Sep 2021, 08:39
yashikaaggarwal wrote:
Simply solve bracket.
(10^-3-10^-5)
= (99/100,000)
Now,
=> 333,333.33*99/100,000
=> 333.33*99
Which is surely slightly less than 333.33
Hence
D is the approximate answer.

Posted from my mobile device


I see an issue within the yellow highlighted portions

1. \(333,333.33 * \frac{99 }{ 100,000}\) will give us \(3.33 * 99\) and not \(333.33\)

2. Plus, \(333.33 * 99\) equals ~ \(33,000\) which is not less than \(333.33\)
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Bunuel
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   03 Nov 2021, 07:57
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Bunuel wrote:
A bar above a digit in a decimal indicates an infinitely repeating decimal. \(333,333.\overline {3}*(10^{–3} – 10^{–5})\) =


A. \(3,333.\overline {3}\)

B. \(3,330\)

C. \(333.\overline {3}\)

D. \(330\)

E. \(0\)




This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   09 Mar 2022, 02:56
BrentGMATPrepNow wrote:
Bunuel wrote:
A bar above a digit in a decimal indicates an infinitely repeating decimal. \(333,333.\overline {3}*(10^{–3} – 10^{–5})\) =


A. \(3,333.\overline {3}\)

B. \(3,330\)

C. \(333.\overline {3}\)

D. \(330\)

E. \(0\)


Key properties:
Multiplying number K by \(10^n\) (where n is positive) moves the decimal place to the RIGHT n spaces.
Multiplying number K by \(10^{-n}\) (where n is positive) moves the decimal place to the LEFT n spaces.

Some examples:
\(1234.567 * 10^{-2} = 12.34567\)
\(123456.7 * 10^{-5} = 1.234567\)
\(8,888,888.\overline {8} * 10^{-4} = 888.\overline {8}\)

Now onto the question!!

We get: \(333,333.\overline {3}*(10^{–3} – 10^{–5}) = 333.\overline {3} - 3.\overline {3}=330\)

Answer: D


BrentGMATPrepNow

Sir
Please help me understanding above part - 3.\overline {3}=330[/m]

thx
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BrentGMATPrepNow
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink] New post   09 Mar 2022, 07:28
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CEO2021 wrote:
BrentGMATPrepNow wrote:
Bunuel wrote:
A bar above a digit in a decimal indicates an infinitely repeating decimal. \(333,333.\overline {3}*(10^{–3} – 10^{–5})\) =


A. \(3,333.\overline {3}\)

B. \(3,330\)

C. \(333.\overline {3}\)

D. \(330\)

E. \(0\)


Key properties:
Multiplying number K by \(10^n\) (where n is positive) moves the decimal place to the RIGHT n spaces.
Multiplying number K by \(10^{-n}\) (where n is positive) moves the decimal place to the LEFT n spaces.

Some examples:
\(1234.567 * 10^{-2} = 12.34567\)
\(123456.7 * 10^{-5} = 1.234567\)
\(8,888,888.\overline {8} * 10^{-4} = 888.\overline {8}\)

Now onto the question!!

We get: \(333,333.\overline {3}*(10^{–3} – 10^{–5}) = 333.\overline {3} - 3.\overline {3}=330\)

ORIGINAL: We get: \(333,333.\overline {3}*(10^{–3} – 10^{–5}) = 333.\overline {3} - 3.\overline {3}=330\)

Answer: D


BrentGMATPrepNow

Sir
Please help me understanding above part - 3.\overline {3}=330[/m]

thx


We want to calculate the value of \(333.\overline {3} - 3.\overline {3}\)

Important: Notice that both numbers have infinitely many 3's after the decimal place.
So, we COULD rewrite the expression as follows: \(333.333333333333333.... - 3.333333333333333....\), at which point all of the 3's after decimal place cancel out to get 330

Here's another way to look at it:
We know that \(\frac{1}{3} = 0.\overline {3}\)

So we can take \(333.\overline {3} - 3.\overline {3}\) and rewrite it as \(333 \frac{1}{3} - 3 \frac{1}{3}\), which simplifies to be \(330\)

Does that help?
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Re: A bar above a digit in a decimal indicates an infinitely repeating dec [#permalink]
09 Mar 2022, 07:28
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