Question

Convert \(-40^{\circ} \mathrm{C}\) to \(^{\circ} \mathrm{F}\) . Show your work.

Short answer

-40°C is equal to -40°F.

Step-by-step solution

Understanding the Formula

To convert temperature from Celsius to Fahrenheit, we can use the conversion formula: \[ F = rac{9}{5}C + 32 \]where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius.

Substitution into the Formula

Substitute \( C = -40 \) into the conversion formula:\[ F = rac{9}{5}(-40) + 32 \]

Perform the Multiplication

Calculate \( \frac{9}{5} imes (-40) = -72 \). This step involves multiplying 9 by -40, and then dividing by 5.

Add to Get Fahrenheit

Now, add 32 to -72 to convert to Fahrenheit:\[ F = -72 + 32 = -40 \]

Conclusion

After performing the calculation, we find that \(-40^{ ext{°C}}\) is equal to \(-40^{ ext{°F}}\).

Key concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is a common task in many scientific and everyday scenarios. And while it might sound complex at first, it actually boils down to a simple mathematical operation. The need for conversion usually arises because different places around the world use different temperature scales. In many countries, Celsius is the standard, whereas in the United States, Fahrenheit is often used.

Learning how to convert temperatures is helpful, whether you're planning a trip abroad, understanding international weather reports, or studying science subjects. With the right approach, anyone can quickly master temperature conversion.

Conversion Formula

At the heart of converting Celsius to Fahrenheit lies a straightforward formula. This formula allows us to translate temperature from one scale to the other with ease. The conversion formula is:

\[ F = \frac{9}{5}C + 32 \]

In this formula, \( F \) stands for the temperature in Fahrenheit, while \( C \) represents the temperature in Celsius. By understanding each component, we simplify the process significantly.

• The fraction \( \frac{9}{5} \) converts the temperature scale due to the differences in the size of the units.
• The number 32 is added to adjust the difference in the starting points of each scale.

Once you grasp this formula, you'll find converting between the two scales becomes second nature.

Step-by-Step Calculation

Let's break down the conversion process into manageable steps to make it clear and approachable. Suppose you want to convert \(-40^{\circ} \mathrm{C}\) to Fahrenheit. Follow these steps:

• Substitute the Celsius value. Start by placing \(-40\) into our conversion formula: \[ F = \frac{9}{5}(-40) + 32 \]
• Perform the multiplication. Calculate \( \frac{9}{5} \times (-40) = -72 \). This involves first multiplying 9 by \(-40\), which gives \(-360\), and then dividing by 5.
• Add 32 to the result. The final step is to add 32 to \(-72\), which equals \(-40\). Hence, \(-40^{\circ} \mathrm{C}\) is equal to \(-40^{\circ} \mathrm{F}\).

Each of these steps builds upon the previous, ensuring clarity and understanding throughout the conversion process.

Negative Temperature Conversion

Negative temperatures can initially appear daunting to convert, but they follow the same rules as positive temperatures. When converting any negative Celsius temperature to Fahrenheit, it's crucial to carefully handle the negative signs.

For instance, with \(-40^{\circ} \mathrm{C}\), the steps are the same as for positive numbers, though the signs differ:

• The multiplication step will result in a negative product since multiplying a positive number \( \frac{9}{5} \) by a negative number \(-40\) results in \(-72\).
• When adding 32 to a negative number like \(-72\), think of it as moving on a number line towards zero from a negative position.

It can be useful to visualize or even draw out the addition on a number line to see the interaction between the numbers. Soon, you'll handle negative temperatures with the same ease as positive ones.