Why is with this obviously wrong math?

July 26, 2010 6:54 AM

If I multiply 1¢ by 10¢ I get 10¢? However, if I use the same monetary amounts and express them as dollars and then multiply them: I get $0.01 * $0.10 = $0.001, which is obviously a different answer to 10¢. I know this is wrong and but how and why?
posted by therubettes to grab bag (18 answers total)

Only one number has a unit - the other number is just the factor you are multiplying by.
posted by cnanderson at 6:56 AM on July 26, 2010 [1 favorite]

You're not multiplying 1cent by 10cents. You are multiplying 10cents by 1 (whole number).
posted by Grither at 6:56 AM on July 26, 2010 [1 favorite]

Multiplying 1 * 10 is not the same thing as multiplying .1 by .01. You just added units in the first example but they didn't actually play into your arithmetic.
posted by proj at 6:56 AM on July 26, 2010 [1 favorite]

That math is right but the units are wrong. The result is not cents or dollars but cents squared and dollars squared. And the conversion between them is not 1 to 100.
posted by smackfu at 6:56 AM on July 26, 2010 [3 favorites]

You can't multiply two ¢ together and get ¢. You would get 10 ¢^2. Similarly, if you multiply $0.01 * $0.10 you would get 0.001 $^2. If you take into account the fact that there are 100 ¢ in every $, 1$^2 is the equivalent of 10,000¢, which is why it makes sense that 10 ¢^2 is equivalent to 0.001$^2.
posted by Phire at 6:57 AM on July 26, 2010 [2 favorites]

You can't really multiply quantities like that. For one, the units are wrong. The answer is not dollars or cents, it is dollars^2 or Cents^2 which makes no sense.

What calculation are you trying to do?
posted by vacapinta at 6:57 AM on July 26, 2010 [1 favorite]

I may be wrong, but I would assume it is because you can't meaningfully multiply by a monetary amount. You can multiply ten cents by one tenth, but not by ten cents. The latter would mean that you want a number of dimes equals to a number of dimes, which is nonsense.
posted by Willie0248 at 6:58 AM on July 26, 2010

You can't multiply ten cents by one cent. You can only multiply ten cents by a factor of one.

Cents are monetary units. Think of them as a pile of gold. You can't multiply a pile of gold by a pile of gold. You can only multiply a pile of gold by a number.
posted by musofire at 6:59 AM on July 26, 2010

What calculation are you trying to do?

This puzzle got me thinking. Answer here

ps fastest ever set of answers!
posted by therubettes at 7:00 AM on July 26, 2010

If I multiply 1¢ by 10¢ I get 10¢? - No. If you multiply 1¢ by 10¢ you get 10¢², and "cents squared" patently don't exist (in a real world, anyway). You can't multiply cents by cents, you multiply them by a number which represents the number of times you want them multiplied.

You mean "If I multiply 1¢ by 10 I get 10¢." Equally, if you multiply $0.01 by 10 you get $0.10.
posted by aqsakal at 7:01 AM on July 26, 2010

Units multiply. Think about it this way: the length of your living room is 10 feet, and the width of your living room is 15 feet. 10 feet x 15 feet = 150 square feet, or foot*foot.

Square cents and square dollars obviously don't have any physical meaning, but you see the same phenomenon when you calculate things like acceleration (meters per square second, which you get by dividing velocity - meters per second - by time, seconds).
posted by backseatpilot at 7:01 AM on July 26, 2010 [4 favorites]

this is why 2ft x 3ft = 6ft^2 which is the same as 24in x 36in = 864 in^2
keep track of the units and all is OK
1cent x 10 cent = 10 cent^2
0.01$ x 0.1$ =0.001 $^2 (one square dollar is (100 x 100) square cents)
posted by youchirren at 7:02 AM on July 26, 2010

Phire is right on. It does make sense if you let the units make sense.

That is, if there were such a thing as square dollars and square cents, then 10 square cents = .001 square dollars. The math is consistent.
posted by vacapinta at 7:02 AM on July 26, 2010

Cents are monetary units. Think of them as a pile of gold. You can't multiply a pile of gold by a pile of gold. You can only multiply a pile of gold by a number.

You can also multiply it by something that is measured in units as long and still end up with an answer in gold (rather than a nonsense unit like square gold) as long as the units cancel out. Like if you had 8 rolls of pennies, and each roll had 50 pennies, you could do 8 rolls * 50¢/roll, which would cause the rolls to cancel, giving you 400¢. The same thing works in dollars 8 rolls * $0.50/roll = $4.

This kind of thing is actually pretty helpful when you are working with physics problems, because if you know that you have to mutliply a set of values and you know the units of all of those values, the unit of the end result (like meters per second squared) just falls straight out of the math.
posted by burnmp3s at 7:22 AM on July 26, 2010 [1 favorite]

This kind of thing is actually pretty helpful when you are working with physics problems, because if you know that you have to mutliply a set of values and you know the units of all of those values, the unit of the end result (like meters per second squared) just falls straight out of the math.
posted by burnmp3s at 10:22 AM on July 26 [+] [!]

And in the reverse, if you know the units of some answer you're trying to find, you can sometimes work backwards to figure out what the derivation* ought to be.

*warning: to be used only in the service of good
posted by heyforfour at 7:37 AM on July 26, 2010 [1 favorite]

Just remember: Rabbits can multiply, but you can't multiply with rabbits (that's just sick), and pennies can't multiply at all.

The only thing you can multiply with is numbers (and good friends, but the latter doesn't work the same way at all.)
posted by Some1 at 10:08 AM on July 26, 2010

So, when you multiply 1 x 10, you're multiplying full numbers. When you're multiplying .01 x .10, you're multiplying decimals- or fractions.

1x10 says, either : 10 sets of this 1 thing, or 1 set of 10. (What is 10 pennies? 10 cents. What is 1 dime? 10 cents).

.01 x .10 says: what is 1/100th of 10 percent? (What is 1 percent of a dime? What is a penny divided by 10?)

Note that these are two VERY different things.
posted by yeloson at 11:03 AM on July 26, 2010

This reminds me of the classic phone call to Verizon customer support. This is mind boggling:

http://verizonmath.blogspot.com/2006/12/verizon-doesnt-know-dollars-from-cents.html
posted by mcschmidt00 at 11:33 AM on July 26, 2010