While I have understood the solution given in OG, I feel there can be a simpler solution

if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ? a. 9 b. 8 c. 7 d. 6 e. 5 Here's one approach: First rewrite the equation as: (0.0015/0.03) x (10^m)/(10^k) = 5 x 10^7 Simplify to get: (0.0015/0.03) x 10^(m-k) = 5 x 10^7 Aside: A quick way to simplify 0.0015/0.03 is to multiply top and bottom by 10,000 to get 15/300. Simplify to get 1/20 So, we now have (1/20) x 10^(m-k) = 5 x 10^7 Isolate 10^(m-k) by multiplying both sides by 20 to get: 10^(m-k) = (20)(5) (10^7) Simplify: 10^(m-k) = (100)(10^7) Simplify: 10^(m-k) = (10^2)(10^7) Simplify: 10^(m-k) = 10^9 So, m-k must equal 9 Answer: A Cheers, Brent

if (0.0015 x 10^m) / (0.03 x 10^k) = (5 x 10^7), then m - k = ? a. 9 b. 8 c. 7 d. 6 e. 5 Let k=0. (0.0015 * 10^m) / (0.03* 10^0) = (5 * 10^7) Convert the decimals to integers: (15 * 10^(-4) * 10^m / (3 * 10^(-2) * 1) = (5 * 10^7) Divide the integers and subtract the exponents: 5 * 10^(-2) * 10^m = 5 * 10^7 Cancel the 5's and divide each side by 10^(-2): 10^m = 10^9 m = 9. Thus: m-k = 9-0 = 9. The correct answer is A.

alt approach .03x.05x10^m/.03x10^k = 5x10^7 5x10^m/10^k+2 = 5x10^7 m-k-2=7 m-k=9

shibsriz@gmail.com wrote:While I have understood the solution given in OG, I feel there can be a simpler solution :( If you plug in k = 2, then the denominator of the fraction just becomes 3. So you'll get an easier equation to solve. If you solve that equation, you'll get m = 11. So then m - k = 11 - 2 = 9.