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11 Nov 2019, 02:26
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C
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Difficulty:
75%
(hard)
Question Stats:
51% (01:54) correct
49%
(01:45)
wrong
based on 1017
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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
(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016
Are You Up For the Challenge: 700 Level Questions
11 Nov 2019, 09:54
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\((1+\frac{1}{500})^4\)= \(1+4C1(1)^3(\frac{1}{500})+ 4C2 (1)^2 (\frac{1}{500})^2+4C3 (1) (\frac{1}{500})^3+4C4 (\frac{1}{500})^4\)
\(6*(\frac{1}{500})^2\)= .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 \((0.004)^2\)
\(6*(\frac{1}{500})^2\)= .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
11 Nov 2019, 10:25
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Bunuel
\(1.002^4 = (1 + 0.002)^4\)
= \( (1 + 0.002)^2*(1 + 0.002)^2 \)
= \((1 + 2*0.002 + 0.002^2)* (1 + 2*0.002 + 0.002^2) \)
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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