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Dollar and penny

Page history last edited by Joe Redish 7 years, 8 months ago

2.1.3.P2

 

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? (Note: It's not enough to say "it's not true." We know that. You need to explain exactly what went wrong with the math. If you're stuck you might consider a similar statement about centimeters and meters.)

 

Joe Redish 9/30/02

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