Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(41^{\circ} \mathrm{C}=\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

41°C is 105.8°F.

Step-by-step solution

Understand the Conversion Formula

The formula to convert Celsius to Fahrenheit is given by \( F = \frac{9}{5}C + 32 \), where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius.

Substitute Given Celsius Value into the Formula

Substitute \( C = 41 \) into the formula. This gives us \( F = \frac{9}{5}\times 41 + 32 \).

Perform the Multiplication of the Fraction

Calculate \( \frac{9}{5} \times 41 \). First, divide 41 by 5 to get 8.2, then multiply by 9 to get 73.8. So, \( \frac{9}{5} \times 41 = 73.8 \).

Add to Convert Into Fahrenheit

Add 32 to the result from Step 3. Therefore, \( 73.8 + 32 = 105.8 \).

Round to the Nearest Tenth

Since the calculation already results in one decimal place, it is \( 105.8 \;^{\circ} \mathrm{F} \). There's no need for further rounding.

Key concepts

Celsius to Fahrenheit

Converting between Celsius and Fahrenheit is a common task in temperature measurement systems. The Celsius scale, also known as centigrade, is widely used around the world, especially in science, while Fahrenheit is often used in the United States for weather-related forecasting and reporting. Knowing how to convert between these two scales can be helpful in various situations, whether you're cooking, traveling, or studying.
To convert a temperature given in Celsius to Fahrenheit, you'll need to use a specific formula. It essentially translates degrees Celsius (°C) into degrees Fahrenheit (°F), helping to maintain accuracy and consistency across temperature readings.

conversion formula

The conversion from Celsius to Fahrenheit involves a straightforward mathematical equation:
\[ F = \frac{9}{5}C + 32 \]
Here:

• \( F \) is the temperature in Fahrenheit.
• \( C \) is the temperature in Celsius.

This formula is derived from the relationship between the two temperature scales, where - Celsius sets the freezing point of water at 0°C and boiling point at 100°C, and Fahrenheit places these points at 32°F and 212°F, respectively.
The fraction \( \frac{9}{5} \) is significant as it aligns the size of one degree Celsius relative to Fahrenheit. The addition of 32 adjusts the offset between scales.
When applying the formula, it's crucial to obey the multiplication and addition operations carefully to avoid errors.
Whether you are converting small, long decimals or simple round numbers, this formula remains reliable and easy to use.

rounding numbers

Rounding numbers is a technique used to simplify number results, helping them become more readable and easier to utilize in practical applications. In this context, rounding to the nearest tenth is required, which seeks to maintain one decimal place.
If the next decimal digit (hundredths place) is 5 or greater, increase the tenths digit by one, rounding up. If it’s 4 or less, keep the tenths digit as it is, rounding down.
For example, in converting 41°C to Fahrenheit, you get 105.8°F. Since the result already perfectly sits at one decimal place, it does not require further adjustment.

• 105.81 would round to 105.8.
• 105.85 (or higher) would round up to 105.9.

Rounding is useful in presenting data cleanly and can be a common requirement in everything from scientific work to everyday temperature conversions.