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Question Number 518 by Yugi last updated on 25/Jan/15

$$Givetheresultofthefollowingcomputationasanintegerintheusualdecimal$$$$form.$$$$\frac{303,000,000,000,303\times 3,300,000,033}{1,000,100,010,001}$$

Answered by prakash jain last updated on 22/Jan/15

$$\frac{303({10}^{12}+1)\times 33\times ({10}^8+1)}{({10}^{12}+{10}^8+{10}^4+1)}$$$$=\frac{303\times 33\times ({10}^{12}+1)({10}^8+1)}{[{10}^8({10}^4+1)+({10}^4+1)]}$$$$=\frac{303\times 33\times [{\left({10}^4\right)}^3+1][{10}^8+1]}{({10}^8+1)({10}^4+1)}$$$$=\frac{303\times 33({10}^4+1)({10}^8-{10}^4+1)}{{10}^4+1}$$$$=303\times 33\times ({10}^8-{10}^4+1)$$$$=9999\times (99990000+1)$$$$=9999\times 9999\times 10000+9999$$$$={(10000-1)}^2\times 10000+9999$$$$=(100000000-20000+1)\times 10000+9999$$$$=(99980000+1)\times 10000+9999$$$$=999800010000+9999$$$$=999800019999$$

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