Final answer:
The signed number to represent the temperature of 50 degrees above zero in Fahrenheit is +50°F. If a cold front reduces this temperature by 40.0 degrees, the new temperature would be +10°F. The Fahrenheit scale sets the freezing point of water at 32°F.
Step-by-step explanation:
To represent the temperature in a signed number format, we start with the temperature value in degrees Fahrenheit. Since the temperature is 50 degrees above 0, and temperatures above zero are considered positive in the context of the Fahrenheit scale, the signed number to represent the temperature is simply +50°F.
If a cold front drops the temperature by 40.0 Fahrenheit degrees, we subtract 40 from the current temperature of +50°F. The new temperature would be +10°F (50 - 40 = 10), still above the freezing point of water on the Fahrenheit scale, which is 32°F. Remember that on the Fahrenheit scale, the interval between the freezing point (32°F) and the boiling point (212°F) is 180 degrees. Thus, a change of 1 degree Fahrenheit is less than a change of 1 degree Celsius because the Celsius scale uses a smaller range (0°C to 100°C) for the same physical change in state of water.