Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(70^{\circ} \mathrm{F}=\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

70°F equals approximately 21.1°C.

Step-by-step solution

Identify the Formula

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

Substitute the Given Value

Insert the given Fahrenheit temperature (70\(^{\circ} \, ext{F} \)) into the formula: \( C = \frac{5}{9} (70 - 32) \).

Calculate the Difference

Perform the subtraction inside the parentheses: \(70 - 32 = 38\). This simplifies the expression to \( C = \frac{5}{9} \times 38\).

Multiply by \(\frac{5}{9}\)

Now multiply 38 by \( \frac{5}{9} \):\(C = \frac{5 \times 38}{9} = \frac{190}{9}\).

Round the Result

Divide 190 by 9 to find \(C\), which is approximately 21.1111. Round this to the nearest tenth to get \(C \approx 21.1\).

Key concepts

Fahrenheit to Celsius Conversion

Understanding how to convert temperatures from Fahrenheit to Celsius is a useful skill, especially when dealing with scientific calculations or traveling abroad. The Fahrenheit scale is commonly used in the United States, whereas Celsius is the standard in most other countries. Knowing how to shift between these two scales can help you adjust to different weather reports or cooking instructions. The conversion process itself is straightforward, once you know the basic formula. By applying this method correctly, you can easily switch between these temperature scales without getting confused.

Conversion Formulas

The conversion formula from Fahrenheit to Celsius is crucial. It can be expressed as:

• \[ C = \frac{5}{9} (F - 32) \]

This equation shows that to find the temperature in Celsius (\(C\)), you need to subtract 32 from the Fahrenheit temperature (\(F\)), then multiply the result by \(\frac{5}{9}\). This scale change accounts for the different starting points and units of measure used in the two systems. The subtraction of 32 is due to the difference in where zero is located on the two scales, and the fraction \(\frac{5}{9}\) accounts for the relative scale stretches.

Math Problem-Solving

To solve a math problem involving temperature conversion, like converting 70 degrees Fahrenheit to Celsius, you simply follow the steps inherent in the conversion formula. First, subtract 32 from the Fahrenheit temperature to account for the base difference. Calculating, \(70 - 32 = 38\). Secondly, you multiply the result by \(\frac{5}{9}\). So, \(\frac{5}{9} \times 38 = \frac{190}{9}\). Understanding each part of the process will help in solving conversion problems for any given Fahrenheit temperature, and reinforcing math problem-solving techniques enhances your calculating efficiency.

Educational Math Steps

Learning temperature conversion through educational steps boosts your comprehension. Breaking down the process into smaller, manageable pieces allows a deeper understanding of each stage. Here's how you can approach it:

• Identify the formula you need for conversion.
• Substitute the given temperature into the formula.
• Perform arithmetic operations carefully, ensuring each step is verified for accuracy.
• Finally, round your answer to the required precision level, which often means to the nearest tenth for temperature problems.

These structured steps simplify the learning process, making it easier to repeat and apply in future conversions or similar mathematical operations.