Temperature (Celsius and Fahrenheit)

Two scales for measuring the same thing

Temperature tells how hot or cold something is. In Mexico and almost everywhere in the world, the Celsius scale (°C) is used. In the United States, the Fahrenheit scale (°F) is used, which belongs to the customary system.

Both scales are set using the same two points of water, but with different numbers:

Between freezing and boiling there are 100 degrees Celsius, but 180 degrees Fahrenheit (212 − 32). That is why one Fahrenheit degree is smaller than one Celsius degree: 100 °C is equivalent to 180 °F, that is, a ratio of $\tfrac{180}{100}=\tfrac{9}{5}$.

From Celsius to Fahrenheit

To convert from °C to °F we do two things, in this order:

1. We multiply by $\tfrac{9}{5}$, because each Celsius degree is worth $\tfrac{9}{5}$ of a Fahrenheit degree.

2. We add 32, because Celsius zero is 32 in Fahrenheit.

From Fahrenheit to Celsius

To go back, we undo the steps in reverse order: first we subtract 32 and then we multiply by $\tfrac{5}{9}$ (the reciprocal of $\tfrac{9}{5}$).

Estimating without a calculator

To know "about" how much it is, there is a quick shortcut: from °C to °F, double it and add 30. From °F to °C, subtract 30 and take half.

With 20 °C: $20\times 2+30=70$ °F. The exact value is 68 °F, pretty close.

Is there a temperature that is the same on both scales?

At 0 °C, Fahrenheit reads 32: it is 32 degrees ahead. But as the temperature drops, Fahrenheit degrees fall faster: for every 1 °C it drops, it is 1.8 °F. So the lead of 32 gets cut down and, at some point below zero, the two numbers meet. We look for $x$ such that $x\,{}^{\circ}C = x\,{}^{\circ}F$. It is solved like a Year 1 equation, with unknowns on both sides.

Summary

Back to the beginning: 14 °F is equivalent to $-10\,{}^{\circ}C$, so Ximena should pack a heavy coat for Chicago.