Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(29^{\circ} \mathrm{C}=\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

\(29^{\circ} \mathrm{C} = 84.2^{\circ} \mathrm{F}\).

Step-by-step solution

Identify the Formula

To convert Celsius to Fahrenheit, we use the formula: \[ F = \left(\frac{9}{5} \times C\right) + 32 \] where F is degrees Fahrenheit and C is degrees Celsius.

Substitute the Given Temperature

Replace \( C \) in the formula with the given temperature, \( 29^{\circ} \mathrm{C} \). This gives us: \[ F = \left(\frac{9}{5} \times 29\right) + 32 \]

Calculate the Multiplication

First, calculate \( \frac{9}{5} \times 29 \) which is part of the formula: \[ \frac{9}{5} \times 29 = 52.2 \]

Add to Complete the Conversion

Now add 32 to the result of the multiplication to get the temperature in Fahrenheit: \[ 52.2 + 32 = 84.2 \]

Round to the Nearest Tenth

The result \( 84.2 \) is already rounded to the nearest tenth. Thus, \( 29^{\circ} \mathrm{C} \) is equivalent to \( 84.2^{\circ} \mathrm{F} \).

Key concepts

Celsius to Fahrenheit

Temperature conversion is a fundamental concept, especially when switching between metric and imperial systems. To convert temperatures from Celsius to Fahrenheit, we use a specific formula. Celsius and Fahrenheit are two units of measurement that define the warmth or coldness of an object. Understanding their conversion is crucial for scientific calculations, cooking, and even daily weather reports. The formula to convert Celsius (C) into Fahrenheit (F) is:
\[ F = \left(\frac{9}{5} \times C\right) + 32\] This formula helps you switch a temperature expressed in degrees Celsius to its equivalent in degrees Fahrenheit.

• The factor \(\frac{9}{5}\) signifies the scale difference between these two units.
• The addition of 32 adjusts the zero point from one scale to another, as water freezes at 0°C but at 32°F.

Knowing this method allows you to easily convert any temperature from one scale to another without needing to memorize multiple values.

Mathematical Formulas

Mathematical formulas are expressions that define relationships between different quantities. In temperature conversion, the formula \( F = \left(\frac{9}{5} \times C\right) + 32 \) specifies how degrees Celsius translate into degrees Fahrenheit. This formula is precise and universally applicable.
To use a mathematical formula effectively:

• Identify the given variables. In our context, \( C \) represents the Celsius temperature.
• Substitute the values for the variable into the formula. Replace \( C \) with the number you wish to convert.
• Perform the operations in the correct order: multiplication first, then addition. This is due to the order of operations rule, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Applying formulas helps solve complex problems step by step and ensures accuracy in scientific and real-world calculations.

Rounding Numbers

Rounding numbers is a mathematical process used to simplify numbers to make them easier to work with or understand. In the context of converting temperatures, specifically when converting to Fahrenheit, we often round to the nearest tenth to make the numbers more manageable and less cumbersome in reports or calculations.
Here’s how you round numbers to the nearest tenth:

• Look at the number in the hundredths place (second decimal place).
• If this number is 5 or greater, increase the number in the tenths place (first decimal place) by 1.
• If it is less than 5, leave the number in the tenths place unchanged.

For instance, in our conversion, when calculating \( 84.2^{\circ}F \), there's no need for additional rounding since the digit after the decimal point is already at the tenth place. Rounding ensures consistency and precision in measurements, facilitating clearer communication of data.