Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(-10^{\circ} \mathrm{C}=\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

-10°C equals 14°F.

Step-by-step solution

Identify the formula

We need to convert Celsius to Fahrenheit. The formula to convert degrees Celsius (°C) to degrees Fahrenheit (°F) is given by \[°F = (°C \times \frac{9}{5}) + 32\]

Plug in the given Celsius temperature

In the formula, substitute \(°C = -10\) to convert to Fahrenheit.\[°F = (-10 \times \frac{9}{5}) + 32\]

Calculate the multiplication

First, multiply \(-10\) by \(\frac{9}{5}\):\[-10 \times \frac{9}{5} = -18\]

Add 32 to the result

Now, add 32 to the result from the multiplication:\[°F = -18 + 32\]

Solve the final step

Solve the addition to find the temperature in Fahrenheit:\[°F = 14\]

Key concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is a common task in everyday life and science. The Celsius scale, which is used primarily in most parts of the world, is based on the freezing and boiling points of water, with 0°C as the freezing point and 100°C as the boiling point. On the other hand, the Fahrenheit scale, mostly used in the United States, sets the freezing point of water at 32°F and the boiling point at 212°F.

The need for conversion arises because various countries and disciplines prefer different scales. Understanding how to switch from one scale to the other easily facilitates communication and helps avoid misunderstanding. It's particularly useful in fields like meteorology, cooking, and international travel.

Mathematical Formula

The mathematical formula to convert a temperature from Celsius to Fahrenheit is straightforward but important to understand. It is given by:

• \[°F = (°C \times \frac{9}{5}) + 32\]

This formula consists of two key operations:

• Multiplying the Celsius temperature by \(\frac{9}{5}\) which scales the Celsius degree into the Fahrenheit scale ratio.
• Adding 32 to account for the offset between the freezing points of the two temperature scales.

The factor \(\frac{9}{5}\) reflects that the Fahrenheit degree is smaller than the Celsius degree, which means there are more Fahrenheit degrees in the same range. Consequently, successful application of this formula allows for seamless translation between the two systems.

Memorizing this equation helps ensure accurate conversions in assignments and real-world scenarios.

Step by Step Calculation

Let's break down the steps to convert -10°C to Fahrenheit using the formula:

• Step 1: Identify the Celsius-to-Fahrenheit formula: Starting with the formula:\[°F = (°C \times \frac{9}{5}) + 32\]
• Step 2: Substitute the Celsius value: Input \(-10°\) for \(°C\) in the formula:\[°F = (-10 \times \frac{9}{5}) + 32\]
• Step 3: Perform the multiplication: Calculate \(-10 \times \frac{9}{5}\), which equals -18.
• Step 4: Complete the addition:Add 32 to the result to obtain \[°F = -18 + 32\].
• Step 5: Solve for Fahrenheit:The finalized conversion is\[14°F\].

This methodical approach clarifies each phase of the conversion, emphasizing accurate substitution and arithmetic. It's crucial in enhancing comprehension and ensuring precision in temperature conversions across various contexts.