What is the closest fraction of an hour it would take a computer operating at 1.026 * 10^15 operations per second to complete 1 million mega-operations?

To determine how long it would take for a computer operating at (1.026 \times 10^{15}) operations per second to complete (1) million mega-operations, we first need to convert the units for consistency.

One mega-operation is equivalent to (10^6) operations. Therefore, (1) million mega-operations is:

[

1 \text{ million mega-operations} = 1 \times 10^6 \times 10^6 = 10^{12} \text{ operations}

]

Next, we calculate how long it would take to perform (10^{12}) operations at a rate of (1.026 \times 10^{15}) operations per second using the formula:

[

\text{Time (in seconds)} = \frac{\text{Total operations}}{\text{Operations per second}}

]

Substituting the values gives us:

[

\text{Time} = \frac{10^{12}}{1.026 \times 10^{15}} \approx \frac{10^{12}}{10^{15}} \times \frac{1}{1.026} = \frac{1}{1.026