A certain computer performs 1.5 × 10^8 calculations per second

A certain computer performs 1.5 × 108 calculations per second. How many seconds would it take this computer to perform 6.0 × 1016 calculations?

  1. 2.5 × 10-9
  2. 9.0 × 100
  3. 4.0 × 102
  4. 4.0 × 108
  5. 9.0 × 1024

Answer

The correct answer is J.

Because the item gives a unit rate, you can set up a proportional relationship and solve for x

(1.5 × 108) / 1 = (6 × 1016) / x

x =  (6 × 1016) / (1.5 × 108)

You can divide the coefficients and subtract the exponents because the bases are the same in each expression.

x = 4.0 × 1016-8

x = 4.0 × 108