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 vaccine at \(4^{\circ} \mathrm{C}\). _______ \({ }^{\circ} \mathrm{F}\)

Short answer

The equivalent temperature is 39.2°F.

Step-by-step solution

Identify the Conversion Formula

To convert a temperature from degrees Celsius (C) to degrees Fahrenheit (F), use the formula: \[ F = \frac{9}{5}C + 32 \]

Substitute the Given Temperature

Insert the given temperature in Celsius (C = 4) into the formula: \[ F = \frac{9}{5} imes 4 + 32 \]

Perform the Multiplication

Calculate the multiplication: \[ \frac{9}{5} imes 4 = 7.2 \]

Add the Constant

Add 32 to the result of the multiplication: \[ F = 7.2 + 32 = 39.2 \]

Round the Result

The result is 39.2. After rounding to the nearest tenth, it remains 39.2.

Key concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is a common task, especially when working with international systems. Both Celsius and Fahrenheit are scales used to measure temperature, but they have different starting points and increments.

• Celsius ( \(^{\circ}C\) ) is widely used in most parts of the world and is based on the freezing (0°C) and boiling points (100°C) of water.
• Fahrenheit ( \(^{\circ}F\) ) is commonly used in the United States. Its freezing point of water is 32°F, and the boiling point is 212°F.

When you need to convert a temperature from Celsius to Fahrenheit, it's essential to know the correct method to ensure accuracy. Understanding this conversion helps in various fields such as science, cooking, and everyday temperature management.

Conversion Formula

The formula to convert Celsius to Fahrenheit is crucial, and it allows you to change any temperature from one scale to another effortlessly. This is the conversion formula:\[ F = \frac{9}{5}C + 32 \]Here's how it works:

• The \(\frac{9}{5}\) factor represents the difference in scale increments between Celsius and Fahrenheit.
• Adding 32 adjusts for the different starting points, aligning the Celsius zero point with 32 degrees Fahrenheit.

For example, if the temperature in Celsius is 4°C, you can substitute it into the formula:\[ F = \frac{9}{5}\times 4 + 32 \]This process is straightforward and gives you the converted temperature in Fahrenheit, which is a valuable skill in situations where temperature settings are critical, such as storing medications or operating equipment.

Rounding Numbers

Rounding numbers is a useful mathematical process to make figures easier to understand and use. It involves adjusting a number to a certain level of precision. Rounding is especially important in scientific and practical applications where overly precise measurements aren't necessary or feasible. When rounding to the nearest tenth:

• Look at the digit in the hundredths place (second digit after the decimal).
• If this digit is 5 or more, increase the tenths place by one.
• If it is less than 5, keep the tenths place number unchanged.

In our temperature conversion example, after calculating the Fahrenheit temperature of 4°C, we got 39.2°F. Observing the calculated number, the tenths place is 2, and since the hundredth place is nothing beyond 2, the rounded number remains 39.2°F. Rounding allows the result to be both precise and easy to communicate, which is important in many practical applications.