Chapter 1, Problem 14P

Throughout the world, the majority of countries use the centigrade scale rather than the Fahrenheit scale. This can cause problems for travelers not familiar with what to expect at certain temperature levels. To alleviate this problem, the following approximate conversion is typically used:

$°\text{F=2}\left(°\text{C}\right)+30°$

Comparing to the exact formula of $°\text{F}=\frac{9}{5}°\text{C+32°}$ we find the ratio $9/5$ is approximated to equal 2, and the temperature of $32°$ is changed to $30°$ simply to make the numbers easier to work with and slightly compensate for the fact that $2\left(°\text{C}\right)$ is more than $9/5\left(°\text{C}\right).$

1. The temperature of $20°\text{C}$
2. is commonly accepted as normal room temperature. Using the approximate formula, determine (in your head) the equivalent Fahrenheit temperature.
3. Use the exact formula and determine the equivalent Fahrenheit temperature for $20°\text{C}$
4. .
5. How do the results of parts (a) and (b) compare? Is the approximation valid as a first estimate of the Fahrenheit temperature?
6. Repeat parts (a) and (b) for a high temperature of $\text{30°C}$
7. and a low temperature of $\text{5°C}\text{.}$