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A student makes the following argument: "I can prove a dollar equals a penny. Since a dime (10 cents) is one-tenth of a dollar, I can write:

10¢ = 0.1 $

Square both sides of the equation. Since squares of equals are equal,

100 ¢ = 0.01 $.

Since 100 ¢ = 1 $ and 0.01 $ = 1 ¢ it follows that 1$ = 1 ¢."

What's wrong with the argument?

Page last modified September 30, 2002: G06