Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(39.6^{\circ} \mathrm{C}=\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

39.6°C is approximately 103.3°F.

Step-by-step solution

Understand the Conversion Formula

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

Insert the Celsius Value into the Formula

Substitute the given temperature in Celsius (\( 39.6^{\circ} \mathrm{C} \)) into the conversion formula. \[ F = \frac{9}{5} \times 39.6 + 32 \]

Perform the Multiplication

Multiply \( 39.6 \) by \( \frac{9}{5} \):\[ \frac{9}{5} \times 39.6 = 71.28 \]

Add 32 to the Result

Add 32 to the product calculated in the previous step to find the temperature in Fahrenheit:\[ 71.28 + 32 = 103.28 \]

Round the Fahrenheit Temperature

Round \( 103.28 \) to the nearest tenth:\[ 103.28 \approx 103.3 \] Thus, the temperature is approximately \( 103.3^{\circ} \mathrm{F} \).

Key concepts

Celsius to Fahrenheit

Celsius and Fahrenheit are two different temperature scales commonly used around the world. However, they measure the same thing—the degree of heat or cold in the atmosphere. Celsius is often used in most parts of the world, while Fahrenheit is commonly used in the United States. Understanding how to convert between these two scales is crucial especially when interacting with international data or travel. When converting Celsius to Fahrenheit, remember that adding a certain number of degrees in one scale doesn’t equate to the same numerical addition in the other. This is because the degree increments between the two scales vary, where one degree Celsius is larger than one degree Fahrenheit.

The Celsius to Fahrenheit conversion is a practical skill that helps in many real-life situations such as cooking, scientific studies, or climate-related conversations. Being adept at this conversion process makes you versatile and able to participate in discussions irrespective of the temperature scale being used.

Conversion Formula

The conversion formula is a mathematical equation used to translate a temperature value from one unit to another, specifically from Celsius to Fahrenheit. It is expressed as:

• \( F = \frac{9}{5}C + 32 \)

This formula relies on the linear relationship between these two temperature scales. As part of its derivation, note that the multiplication factor \( \frac{9}{5} \) represents how the temperature scales align with each other incrementally.

The "32" in the formula accounts for the starting point difference on each scale (since 0°C corresponds to 32°F based on where water freezes). When applying this formula, it's vital to follow the order of operations where multiplication is performed first, followed by addition to get the result in Fahrenheit. This will ensure precise conversions and accurate results. Using this formula helps you seamlessly switch between temperature scales without confusion.

Rounding Temperatures

When dealing with temperature conversion, it’s often necessary to round your answers to a specific number of decimal places for clarity and conciseness. In this exercise, we are asked to round to the nearest tenth, which means we retain only one digit after the decimal point. For example, converting 39.6°C to Fahrenheit yields 103.28°F. To round it to the nearest tenth, you look at the digit in the hundredths place (which is 8 in this case).

Given that this digit is 5 or more, you round the preceding tenths digit up by one, resulting in 103.3°F. Rounding is particularly important in many fields, such as meteorology and laboratory settings, where precision in measurement directly impacts decisions. Practicing temperature rounding ensures clarity in communication and prevents unnecessary complexity in numerical data.

Mathematical Operations

Performing mathematical operations is a key component in temperature conversions. It involves basic arithmetic skills such as multiplication, addition, and sometimes subtraction or division. For Celsius to Fahrenheit conversion, after identifying the appropriate conversion formula, the primary operations include:

• Multiplying the Celsius value by the fraction \( \frac{9}{5} \).
• Adding 32 to the result of the multiplication.

These operations are fairly straightforward, requiring attention to the sequence to avoid errors.

The order of operations warrants multiplication before addition, which ties back to performing calculations correctly as highlighted by the BODMAS/BIDMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Mastering these fundamental operations is essential, as it allows you to effectively apply the conversion formula and adjust temperatures between Celsius and Fahrenheit accurately.