Accepted answer
Answer included
Goal. Convert 38.4°C into degrees Fahrenheit using the
standard Celsius to Fahrenheit conversion.
Conversion formula
Celsius (°C) and Fahrenheit (°F) are related by a linear transformation:
\[
F=\frac{9}{5}C+32
\]
The factor \(\frac{9}{5}\) rescales the Celsius degree size to Fahrenheit degrees, and the \(+32\) accounts for the different zero points of the two temperature scales.
Step-by-step calculation for 38.4°C
-
Substitute \(C=38.4\) into the formula:
\[ F=\frac{9}{5}(38.4)+32 \]
-
Multiply by \(\frac{9}{5}\) (equivalently \(1.8\)):
\[ \frac{9}{5}(38.4)=1.8\cdot 38.4=69.12 \]
-
Add 32:
\[ F=69.12+32=101.12 \]
Result. The value of 38.4 celsius to fahrenheit is
101.12°F, which rounds to 101.1°F (to one
decimal place).
Rounded results at common precisions
| Reporting precision | Fahrenheit value | How it is obtained |
|---|---|---|
| Exact (to 2 decimals) | 101.12°F | Direct evaluation of \(F=\frac{9}{5}C+32\) |
| One decimal place | 101.1°F | \(101.12\) rounded to the nearest tenth |
| Nearest whole degree | 101°F | \(101.12\) rounded to the nearest integer |
Visualization of the conversion line
Frequent conversion errors
- Using the inverse relation by mistake: Fahrenheit to Celsius is \(C=\frac{5}{9}(F-32)\).
- Dropping the offset term \(+32\), which shifts the Fahrenheit scale relative to Celsius.
- Rounding before finishing the arithmetic; compute the product and addition first, then round once.
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