Question

For each of the following statements, change the given temperature to its corresponding equivalent in \({ }^{\circ} \mathrm{C}\) or \({ }^{\circ} \mathrm{F}\). (Round to the nearest tenth.) Store medication within temperature range of \(15^{\circ} \mathrm{C}\) to \(30^{\circ} \mathrm{C}\). _______ \({ }^{\circ} \mathrm{F}\)

Short answer

The range is 59°F to 86°F.

Step-by-step solution

Identify the temperature conversion formula

We need to convert temperatures from Celsius to Fahrenheit. The formula for converting Celsius (\(C\)) to Fahrenheit(\(F\)) is:\[F = \frac{9}{5} \times C + 32\]

Convert the lower limit of the range

Substitute \(C = 15\) into the formula:\[F = \frac{9}{5} \times 15 + 32 = 27 + 32 = 59^\degree\mathrm{F}\]The lower limit of the temperature range is \(59^\degree\mathrm{F}\).

Convert the upper limit of the range

Substitute \(C = 30\) into the formula:\[F = \frac{9}{5} \times 30 + 32 = 54 + 32 = 86^\degree\mathrm{F}\]The upper limit of the temperature range is \(86^\degree\mathrm{F}\).

Combine the converted range

Combine the converted lower and upper limits to express the full temperature range in Fahrenheit:\(59^\degree\mathrm{F}\) to \(86^\degree\mathrm{F}\).

Key concepts

Celsius to Fahrenheit conversion

Converting temperatures from Celsius to Fahrenheit is a common requirement in science, cooking, and daily life. The conversion helps unify temperature reporting across different regions that use different scales.
To convert a temperature from Celsius (\(^\circ\mathrm{C}\)) to Fahrenheit (\(^\circ\mathrm{F}\)), use the formula:\[F = \frac{9}{5} \times C + 32\]
This equation multiplies the Celsius value by 9/5 and then adds 32. This transformation accounts for the difference in zero points and the size of each degree on the two scales. For instance, when converting 25°C, you multiply by 1.8 (which is 9/5) and then add 32, resulting in 77°F.

temperature range conversion

When dealing with scenarios that require understanding a range of temperatures, such as in weather forecasts or setting thermostat limits, it's crucial to convert the entire range accurately.
For example, converting the range of 15°C to 30°C to Fahrenheit involves calculating both endpoints individually. Using the formula for each limit ensures the entire spectrum is clear and correctly redefined in the new units.

• Lower limit: Convert 15°C to Fahrenheit using \(F = \frac{9}{5} \times 15 + 32\) to get 59°F.
• Upper limit: Convert 30°C to Fahrenheit using \(F = \frac{9}{5} \times 30 + 32\) to get 86°F.

Thus, the temperature range of 15°C to 30°C converts to 59°F to 86°F.

medication storage temperature

Medications often require specific storage conditions to maintain their efficacy and safety. One crucial aspect is maintaining the correct temperature range.
For many medications, like those stored between 15°C and 30°C, staying within this range ensures the active ingredients remain effective. For health professionals and patients, knowing the equivalent Fahrenheit range is equally important when living in regions using that scale.
In this example, a storage requirement of 15°C to 30°C translates to 59°F to 86°F, ensuring proper storage whether you're using Fahrenheit or Celsius.

temperature conversion formula

Understanding the temperature conversion formula is essential for accurate conversions between Celsius and Fahrenheit.
The formula, \[F = \frac{9}{5} \times C + 32\], applies a scaling factor of \(9/5\) and adjusts for the starting point difference between the two scales (32 being the freezing point of water in Fahrenheit compared to 0 in Celsius).
This formula allows one to accurately convert any given temperature in Celsius to its Fahrenheit counterpart, aiding in a variety of practical settings, such as engineering, environmental science, and international travel.