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UB001
Joined: 26 Dec 2018
Last visit: 10 Apr 2022
Posts: 106
Given Kudos: 91
Location: India
Schools: Mannheim"20 Smurfit "20 NUS '21 NTU '20
31 Dec 2018, 04:07
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (01:50) correct
32%
(01:51)
wrong
based on 293
sessions
History
Date
Time
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Not Attempted Yet
If the digits 53 in the decimal 0.00053 repeat indefinitely, what is the value of (10^5-10^3)(0.00053)?
A. 0
B. 0.53 repeating
C. 5.3
D. 10
E. 53
A. 0
B. 0.53 repeating
C. 5.3
D. 10
E. 53
KanishkM
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Schools: DeGroote'21 Desautels '21 NUS '21
31 Dec 2018, 04:22
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UB001
(10^5-10^3)(0.00053)
when you solve the (10^5-10^3) part it will become 1000 * 99 which is multiplied with 0.000535353....
= 99*0.535353
giving an answer as 52.37 or something which will be greater than 52.
When you notice this trend the answer will be as E.
UB001
We know how to deal with recurring decimals. Say,
\(.000535353... = x\)
\(.535353... = 1000x\) ... (I)
\(53.535353... = 100000x\) ... (II)
(II) - (I)
\((100000 - 1000)x = 53\)
\(x = \frac{53}{(10^5 - 10^3)}\)
So we get that \(0.000535353... = \frac{53}{(10^5 - 10^3)}\)
Let's put it in our original expression:
\((10^5-10^3)(0.00053) = (10^5-10^3)*\frac{53}{(10^5 - 10^3)} = 53\)
Answer (E)
