Which of the following is equal to 0.9998^2 ?

A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024

M15-07

Dear Hitesh,

You see the difference between the numbers starts from the last but one digit. So it is enough to multiply and get the last two digits only. Here in the case of 0.9998 x 0.9998, multiply only 98 and 98, you get 9604. The last but one digit is 0 which is only in choice C.
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Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

\((0.9998)^2=(1-0.0002)^2=(1-2*10^-^4)^2=1+2^2*10^-^8-2*2*10^-^4\) it's the old formula \((a+b)^2=a^2+b^2+2ab\)

\(1+4*10^-^8-4*10^-^4=1+0.00000004-0.0004\)

\((1-0.0004)+0.00000004\)
\(0.9996+0.00000004=0.99960004\)
C
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It just faster to do criss cross multiplication in this question and you can get the answer in less than 30 secs.

9 9 9 8

9 9 9 8

Units place : 8 x 8 = 64 => Units place is 4 with carry over of 4

Tens place : 9x8 + 9x8 + 6 = 150 => Tens place is 0 with carry over of 15

You can stop here since you have already found answer by checking options

This is criss cross multiplication technique from vedic mathematics (http://www.brighthubeducation.com/homew ... thematics/) and i would highly recommend looking it up.

Elaborating 100's place : 9x8 + 9x9 + 9x8 +15 = 240 => 100s place is 0 with carry over 24

1000 place : 9x8 +9x9 + 9x9 + 9x8 + 24 = 330 => 1000 place is 0 with carry over 33 and so on....
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0.9998
0.9998
______
84
82
______
04 in the end

only C

Just for sake of convenience, remove decimal from the question as well from the answer

\(9998^2 = (10^4 - 2)^2 = 100000000 + 4 - 40000 = 100000004 - 40000\)

Last 2 digits are 04

Answer = C
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