Read the sign before the size
- The idea
- Predict
- See it
- Why
- Check
The idea
“The bigger the digits, the bigger the value, so -0.8 is more than -0.3.”
Your eye goes to the digits, and 8 beats 3. The minus sign in front flips the order, so -0.8 is the lower value.
The short version
The mistake: The bigger the digits, the bigger the value, so -0.8 is more than -0.3.
What's actually true: The sign gives direction and the digits give size. A negative value further from zero is lower, and a negative change is a loss.
- Pure water in an open beaker sits at 0 MPa. Solutes pull water potential below zero, so a cell at -0.8 MPa is further below pure water than one at -0.3.
- Free energy reads the same way. A reaction with a ΔG of -45 kJ/mol releases more energy than one at -15. A positive ΔG means energy has to be put in.
- For a change, the sign is the direction. Cells whose mass changed by -10% lost water. Cells at +10% gained it.
On the exam: Check the sign before the size. Under zero, bigger digits mean a lower value or a bigger loss.