UpStudy Free Solution:

To convert a temperature from Celsius (\(^ \circ \)C) to Fahrenheit (\(^ \circ \)F), you can use the following formula:

\[^ \circ F = \frac { 9} { 5} \times ^ \circ C + 32\]

Given \(38.2^ \circ \)C, let's plug it into the formula:

\[^ \circ F = \frac { 9} { 5} \times 38.2 + 32\]

First, perform the multiplication:

\[\frac { 9} { 5} \times 38.2 = 1.8 \times 38.2 = 68.76\]

Then, add 32:

\[68.76 + 32 = 100.76\]

So, \(38.2^ \circ \)C is equal to \(100.76^ \circ \)F.

Supplemental Knowledge

Temperature conversion between Celsius and Fahrenheit is a common task in various scientific and everyday contexts. Understanding the relationship between these two scales is crucial for accurate temperature reporting and interpretation. Here are some additional details:

1. Temperature Scales:

- Celsius (°C): The Celsius scale, also known as the centigrade scale, is used worldwide for most temperature measurements. It is based on the freezing point of water at 0°C and the boiling point at 100°C under standard atmospheric conditions.

- Fahrenheit (°F): The Fahrenheit scale is primarily used in the United States. It sets the freezing point of water at 32°F and the boiling point at 212°F under standard atmospheric conditions.

2. Conversion Formula:

- To convert from Celsius to Fahrenheit:

\[^ \circ F = \frac { 9} { 5} \times ^ \circ C + 32\]

- To convert from Fahrenheit to Celsius:

\[^ \circ C = \frac { 5} { 9} \times ( ^ \circ F - 32) \]

3. Example Calculation:

Suppose you want to convert \(25^ \circ \)C to Fahrenheit:

\[^ \circ F = \frac { 9} { 5} \times 25 + 32 = 45 + 32 = 77^ \circ F\]

4. Understanding the Formula:

- The factor \(\frac { 9} { 5} \) accounts for the different sizes of degrees on the two scales.

- Adding or subtracting 32 adjusts for the different starting points of each scale.

5. Applications:

- Weather forecasting often requires converting temperatures between these scales.

- Scientific experiments may need conversions depending on regional measurement preferences.

6. Historical Context:

- The Celsius scale was developed by Anders Celsius in the early 18th century.

- The Fahrenheit scale was developed by Daniel Gabriel Fahrenheit around the same time period.

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