How many hours are required for a radio signal from a space probe near the dwarf planet Pluto, 6.00 x 10 (to the 9th) km away, to reach Earth? Assume that the radio signal travels at the speed of light, 3.00 10 (to the 8th) m/s.

To calculate the time required for a radio signal to travel from Pluto to Earth, we need to convert the distance between them into meters, as the speed of light is commonly given in meters per second.

Given:
Distance from Pluto to Earth = 6.00 x 10^9 km
Speed of light = 3.00 x 10^8 m/s

The first step is to convert the distance from kilometers to meters:
6.00 x 10^9 km = 6.00 x 10^9 x 10^3 m = 6.00 x 10^12 m

Now we have the distance in meters.

Next, we can use the equation:
Time = Distance / Speed

Time = (6.00 x 10^12 m) / (3.00 x 10^8 m/s)

To simplify the calculation, we can cancel out the common factor of 10^8 in the numerator and denominator:

Time = (6.00 x 10^12) / (3.00 x 10^8) = 2.00 x 10^4 s

We now have the time in seconds.

To convert this to hours, we can divide the seconds by the number of seconds in an hour:
1 hour = 60 minutes x 60 seconds = 3600 seconds

Time (in hours) = (2.00 x 10^4 s) / (3600 s/hour) = 5.5556 hours (rounded to 4 decimal places)

Therefore, it would take approximately 5.556 hours for a radio signal from a space probe near Pluto to reach Earth.