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23 Aug 2017, 01:24
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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. \(10^{21}\)
A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)
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23 Aug 2017, 02:34
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MathRevolution
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. \(10^{21}\)
\(11*10^{20}–9*10^{10}\)A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)
We can use approximate value. Hence we can use \(10\) in place of \(11\) and \(10\) in place of \(9\).
\((10*10^{20}) – (10*10^{10})\)
\(10^{(20+1)}–10^{(10+1)}\)
\(10^{21}–10^{11}\)
\(10^{11}(10^{10}–1)\)
\(1\) is very small value compared to \(10^{10}\). Hence \(1\) can be ignored. Therefore \((10^{10}–1) =\) approximately \(= 10^{10}\)
\((10^{11})(10^{10})\)
\(10^{(11+10)}\) \(= 10^{21}\)
Answer (E)...
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23 Aug 2017, 05:39
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We have been asked to find the value of the expression \(11*10^{20}–9*10^{10}\)
\(11*10^{20}–9*10^{10}\)
= \(11*10^{10}*10^{10} – 9*10^{10}\)
= \(10^{10}(11*10^{10} – 9)\)
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)
\(11*10^{20}–9*10^{10}\)
= \(11*10^{10}*10^{10} – 9*10^{10}\)
= \(10^{10}(11*10^{10} – 9)\)
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)
