### Brain Teasers

# Dollar and Cents

What is wrong with the following logic that "proves" 1 dollar = 1 cent? See if you can determine at which line(s) a mistake is made.

1 dollar

= 100 cents

= 10 cents x 10 cents

= 1/10 dollar x 1/10 dollar

= 1/100 dollar

= 1 cent

1 dollar

= 100 cents

= 10 cents x 10 cents

= 1/10 dollar x 1/10 dollar

= 1/100 dollar

= 1 cent

### Hint

Try replacing money (dollar and cent) with length (metre and centimetre).What is 10cm x 10cm?

### Answer

The chain of equality breaks down at the second equals sign.10 cents x 10 cents = 100 cents^2 (whatever a square cent is). It's like mixing length (metres) with area (square metres).

It should read 100 cents = 10 x 10 cents.

The same type of error is made again when dollar x dollar is asserted equal to dollar instead of dollar^2.

Here is corrected logic:

1 dollar

= 100 cents

= 10 x 10 cents

= 10 x 1/10 dollar

= 10/10 dollar

= 1 dollar

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