# A dollar, a penny, there's no difference

Sam is a gluttonous kid, so he decides to buy a colorful lollipop at the price of 1\$ (one dollar) in the nearest candy store. Though, he realizes that he can't afford it as his budget is just 1ยข (a penny). Anyway, Sam isn't going to give up, so he asks to his friend Tom to change his penny with a dollar.

Sam replies: "One dollar is 100 pennies; 100 pennies are 10 pennies x 10 pennies; 10 pennies x 10 pennies are 1/10 of dollar x 1/10 of dollar; 1/10 of dollar x 1/10 of dollar is 1/100 of dollar; I just showed you that one dollar is equivalent to a penny."

How is Sam lying?

• Sam is lying by saying something that he knows to be untrue as if it were true. – KSmarts Apr 2 '15 at 21:56

Sam is simply mixing up the units: dollars, squares of dollar, pennies, squares of pennies. This yields a lot of nonsense.

Sam replies: "100 pennies are 10 pennies x 10 pennies."

This statement is wrong: 10 pennies x 10 pennies equals 100 penny-squared.
(A correct statement would be: 10 times 10 pennies equals 100 pennies.)

"1/10 of dollar x 1/10 of dollar is 1/100 of dollar"

This is also wrong: 1/10 of dollar x 1/10 of dollar equals 1/100 dollar-squared.

• I wonder how much a dollar-squared is worth. – Kruga Mar 10 '16 at 10:26
• @Kruga. At today's exchange rate is worth 0.7921 squared euros. – Marius Aug 29 '16 at 6:36