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Since we need an approximate value and the overall expression has extremely large numbers, we can assume both 11 and 9 to be equal to 10

The expression now becomes \(10^{10}(10*10^{10} – 10) = 10^{10}*10^1(10^{10} – 1) = 10^{10+1}(10^{10} – 1)\) = \(10^{11}(10^{10})\)

Since a difference of 1 does not influence the value of the expression to that extent, the value must be \(10^{21}\) approximately (Option E) _________________

Which of the following is the closest to 11*1020–9*1010? [#permalink]

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23 Aug 2017, 19:26

MathRevolution wrote:

Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\) B. \(10^7\) C. \(10^{10}\) D. \(10^{20}\) E. \(10^{21}\)

1. Factoring \(10^{10}\) out = \(10^{10} (11*10^{10} - 9)\) 2. Since we are asked about approximation, so we can use our estimation. 3. 11 and 10 is closest to 10, so I can change them to 10 --> \(10^{10} (10^1*10^{10} - 10^1)\) --> \(10^{10} (10^{11} - 10^1)\) 4. Difference between \(10^{11}\) and \(10^{10}\) is so HUGE, so can we can IGNORED this subtraction by \(10^1\). 5. Therefore, \(10^{10} * 10^{11} = 10^{21}\).

=> \(9*10^{10}\) is a relatively small number compared with \(11*10^{20}\). \(11*10^{20}–9*10^{10}\) is approximate to \(11*10^{20}\), which is similar to \(10^{21}\).

Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\) B. \(10^7\) C. \(10^{10}\) D. \(10^{20}\) E. \(10^{21}\)

Since 9 x 10^10 is much smaller than 11 x 10^20, magnitude-wise, subtracting it from 11 x 10^20 would still be about 11 x 10^20. Since 11 is close to 10, 11 x 10^20 is approximately 10 x 10^20, magnitude-wise, and we have:

10 x 10^20 = 10^21

Answer: E
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