A certain computer performs `1.5 xx 10^(8)` calculations per second. How many seconds would it take this computer to perform `6.0 xx 10^(16)` calculations?

Options

A. `2.5 xx 10^(-9)`
B. `9.0 xx 10^(0)`
C. `4.0 xx 10^(2)`
D. `4.0 xx 10^(8)`

Answer

To solve the problem of how many seconds it would take for a computer that performs \(1.5 \times 10^8\) calculations per second to perform \(6.0 \times 10^{16}\) calculations, we can follow these steps:

### Step 1: Understand the problem
We know the rate of calculations the computer can perform and the total number of calculations needed. We need to find out how many seconds it will take to complete those calculations.

### Step 2: Set up the equation
Let \( T \) be the time in seconds required to perform \( 6.0 \times 10^{16} \) calculations. The formula to find time when you know the total calculations and the rate of calculations is:
\[ T = \frac{\text{Total calculations}}{\text{Calculations per second}} \]

### Step 3: Substitute the values
Substituting the given values into the equation:
\[ T = \frac{6.0 \times 10^{16}}{1.5 \times 10^{8}} \]

### Step 4: Simplify the fraction
Now, we can simplify the fraction:
1. Divide the coefficients:
\[ \frac{6.0}{1.5} = 4.0 \]
2. For the powers of 10, we use the property of exponents:
\[ \frac{10^{16}}{10^{8}} = 10^{16 - 8} = 10^{8} \]

So, we can rewrite \( T \):
\[ T = 4.0 \times 10^{8} \]

### Step 5: Final answer
Thus, the total time \( T \) it would take for the computer to perform \( 6.0 \times 10^{16} \) calculations is:
\[ T = 4.0 \times 10^{8} \text{ seconds} \]