10^8- 10^2/10^7 - 10^3 = ?
A) 0
B) 1
C) 10
D) 10^2
E) 10^3
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10^8- 10^2 = 10^2(10^6 - 1)
10^7 - 10^3 = 10^3(10^4 - 1)
10^8- 10^2/10^7 - 10^3 = [10^2(10^6 - 1)]/[10^3(10^4 - 1)]. Simplify 10^2 and you get (10^6 - 1)/(10^5 - 10). Since we're dealing with fairly large numbers, we can estimate 10^6 - 1 with 10^6 and 10^5 - 10 with 10^5. In the end you get that your initial fraction is closest to 10^6/10^5 = 10.
Answer C.
10^7 - 10^3 = 10^3(10^4 - 1)
10^8- 10^2/10^7 - 10^3 = [10^2(10^6 - 1)]/[10^3(10^4 - 1)]. Simplify 10^2 and you get (10^6 - 1)/(10^5 - 10). Since we're dealing with fairly large numbers, we can estimate 10^6 - 1 with 10^6 and 10^5 - 10 with 10^5. In the end you get that your initial fraction is closest to 10^6/10^5 = 10.
Answer C.
