enter image description here

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

  • 5
    $\begingroup$ Yes, the units don’t match across the 2nd equals sign $\endgroup$ – Alex Mar 12 at 0:20
  • 2
    $\begingroup$ 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. $\endgroup$ – Dean Young Mar 12 at 0:20

$\$0.01=(\sqrt{\$}0.1)^2$, not $(\$0.1)^2$.


You can clearly see the fallacy if you keep track of the units:

  • 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 $(10c)^2=100c^2$.

In conclusion, two equalities are bogus, and so is the argument.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.