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Rounded to three decimal places, 1.002^4 =

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Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 11 Nov 2019, 02:26
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

34% (01:31) correct 66% (01:43) wrong based on 80 sessions

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Re: Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 11 Nov 2019, 07:28
1
Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


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1.002^4 = ~ 1.008
IMO C
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Re: Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 11 Nov 2019, 09:54
1
\((1+\frac{1}{500})^4\)= \(1+4C1(1)^3(\frac{1}{500})+ 4C2 (1)^2 (\frac{1}{500})^2+4C3 (1) (\frac{1}{500})^3+4C4 (\frac{1}{500})^4\)

\(6*(\frac{1}{500})^2\)= .0000015
This is so small that we can neglect it or any higher power of (1/500)

Hence, neglect third, fourth and fifth term of the binomial expansion.

\(1.002^4 =\) \(1+\frac{4}{500}\)=1.008

OR

If you're not familiar with the binomial expansion, you can write \((1.002)^4= (1.002)^2 *(1.002)^2\)

\((1+0.002)^2= 1+2*1*0.002+(0.002)^2\)= 1.004......as we can neglect \((0.002)^2\)

\((1.002)^4= (1.004)^2\)

\((1+0.004)^2= 1+2*1*0.004+(0.004)^2\)= 1.008......as we can neglect \((0.004)^2\)




Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


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Re: Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 11 Nov 2019, 10:25
1
Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


Are You Up For the Challenge: 700 Level Questions


\(1.002^4 = (1 + 0.002)^4\)
= \( (1 + 0.002)^2*(1 + 0.002)^2 \)
= \((1 + 2*0.002 + 0.002^2)* (1 + 2*0.002 + 0.002^2) \)
Neglect \( 0.002^2 (= 0.000004) \)
= \((1 + 0.004)*(1 + 0.004) \)
= \((1 + 0.004)^2 \)
= \( 1 + 2*0.004 + 0.004^2 \)
= \( 1 + 0.008 + 0.000016 \)
= \( 1.008016 \)

Rounded to 3 decimal places = 1.008

IMO Option C

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Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 14 Nov 2019, 22:03
Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


Are You Up For the Challenge: 700 Level Questions


Step 1: calculate (1.002)^2 = 1 + (0.002)^2+ 2*(0.002) = 1.004 (because we want only first 3 digits and square of 0.002 will be 6 digits).
Step 2: calculate 1.004^2 = 1 + 0.008 = 1.008 (using the same logic as in step 1).

Ans = 0.008, Option C
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Re: Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 20 Nov 2019, 02:19
1
Archit3110 wrote:
Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


Are You Up For the Challenge: 700 Level Questions



1.002^4 = ~ 1.008
IMO C


Did you use a calculator? or is there some trick to visualize this.
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Re: Rounded to three decimal places, 1.002^4 =  [#permalink]

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New post 20 Nov 2019, 02:25
We can write this fraction as a binomial -
(1+0.002)^4. now applying approximation,
we have (1+x)^n = 1 + n*x + \(\frac{n(n-1)}{2}\)*x^2
so, our expression becomes =

1 +4*0.002 + \(\frac{4*3}{2}\)*(0.002)^2
The third term is very small and the number can be approximated to
1.008

OA - C
Bunuel wrote:
Rounded to three decimal places, \(1.002^4 =\)

(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016


Are You Up For the Challenge: 700 Level Questions
GMAT Club Bot
Re: Rounded to three decimal places, 1.002^4 =   [#permalink] 20 Nov 2019, 02:25
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