# What's wrong with this bogus proof?

What is the mistake here? Is it matter of the unit?

• Yes, the units don’t match across the 2nd equals sign – Alex Mar 12 at 0:20
• Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred. – Dean Young Mar 12 at 0:20

$$\0.01=(\sqrt{\}0.1)^2$$, not $$(\0.1)^2$$.
• In the second equality, $$\0.01 = \0.1\times \0.1$$ is not true, if you are doing units.
• Even if the second equality were true, the third one gives problems: since $$c=\/100$$, you have $$(\0.1)^2=\left(\frac c{100}\,0.1\right)^2=\frac{c^2}{100}\times\frac1{10}=\frac{c^2}{1000}.$$ This is not $$(10c)^2=100c^2$$.