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In recent a chip can compute 1.026*1015 operations per 1 second. How m

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In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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In recent a chip can compute \(1.026 \times 10^{15}\) operations per 1 second. How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)

A. \(3 \times 10^{-5}\)
B. \(3 \times 10^{-6}\)
C. \(3 \times 10^{-7}\)
D. \(3 \times 10^{-8}\)
E. \(3 \times 10^{-9}\)

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Originally posted by MathRevolution on 10 Jan 2016, 18:36.
Last edited by mikemcgarry on 07 Feb 2017, 12:13, edited 2 times in total.
Reformatted the question to proper mathematical notation.
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Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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New post 10 Jan 2016, 20:18
MathRevolution wrote:
In recent a chip can compute 1.026*1015 operations per 1 second. How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)



A. 3*10-5
B. 3*10-6
C. 3*10-7
D. 3*10-8
E. 3*10-9



*A solution is going to be uploaded in two days.


Hi,
the Q if done the way it is written does not find an answer in the choice...
some Typo error may be...
1 million mega operations= 10^6*10^6=10^12..
1.026*1015 nearly 10^3 operations in 1 sec...
10^3 *3600 in 1 hour..
1 op in 1/(10^3 *3600 )...
10^12 op in 10^12/(10^3 *3600 )...
10^9/3600= nearly 3*10^5...
ans A, if 10-5 was meant to be 10^5....
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Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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New post 12 Jan 2016, 18:43
1
How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)
A. 3*10-5 B. 3*10-6 C. 3*10-7 D. 3*10-8 E. 3*10-9


→ From 1.026*10^16:1 sec=1 million mega-operation:n=10^6*10^6:n, it becomes n=10^12/1.026*10^15 sec. That is, 10^12/1.026*10^15 sec=10^12/(1.026*10^15*3,600)hr=3*10^-7 hr. Therefore, the answer is C.
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Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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New post 13 Jan 2016, 13:52
3
MathRevolution wrote:
How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)
A. 3*10-5 B. 3*10-6 C. 3*10-7 D. 3*10-8 E. 3*10-9


→ From 1.026*10^16:1 sec=1 million mega-operation:n=10^6*10^6:n, it becomes n=10^12/1.026*10^15 sec. That is, 10^12/1.026*10^15 sec=10^12/(1.026*10^15*3,600)hr=3*10^-7 hr. Therefore, the answer is C.


I was about to support and reiterate Chetan4u's solution, but then I figured out where the typo is in the question!

The question is supposed to read:
A new computer chip can compute \(1.026*10^{15}\) operations per second. How many hours will it take the chip to compute 1 million mega-operations (mega-operations=1 million operations)?

A. \(3*10^{-5}\)
B. \(3*10^{-6}\)
C. \(3*10^{-7}\)
D. \(3*10^{-8}\)
E. \(3*10^{-9}\)



Now we can answer the question the way it was intended.

We are told that a computer chip can perform \(1.026*10^{15}\) operations per second, and we are asked how many hours it will take for the ship to perform one million million operations (\(10^{12}\) operations). Since each of the answer choices are separated by a power of 10, then we can safely approximate \(1.026*10^{15} = 1*10^{15}\).

We can find the number of seconds it will take to perform \(10^{12}\) operations by dividing the number of operations by the number of operations per second:

\(\frac{12^{12}}{10^{15}} = 10^{-3}\) seconds.

Now to convert seconds to hours, we need to divide \(10^{-3}\) seconds by 3600 seconds per hour. Again, since the answer choices are spread out by powers of 10, we can approximate:

\(\frac{10^{-3}}{3.6*10^3} = \frac{10^{-6}}{3.6} ≈ 3*10^{-7}\)

So the answer should be C

Clear notation, like punctuation, makes all the difference...
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Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m   [#permalink] 29 Sep 2018, 11:11
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