Metres Squared and Square MetresDate: 05/02/2003 at 07:38:55 From: Nigel Knowles Subject: Metres Squared and square metres In Meters Squared vs. Square Meters http://mathforum.org/library/drmath/view/57209.html you have said that square metres and metres squared are the same thing, but this cannot be the case. If I have an square area of 5m x 5m this is actually termed 25 square metres. But you state this can also be called 25 metres squared. But surely 25 metres squared is 25m x 25m, which is 625 square metres? How do I write either of these down to avoid confusion? Date: 05/02/2003 at 08:16:31 From: Doctor Ian Subject: Re: Metres Squared and square metres Hi Nigel, When we say 25 m^2 we mean 25 (m^2) That is, following the conventional order of operations, we evaluate the exponent first, so it applies only to the units. That's different from (25 m)^2 = 25^2 m^2 Consider the expression 5 + 3x^2 You don't interpret that as (3x)^2, right? Same thing here. > How do I write either of these down to avoid confusion? You have to be careful about where you put the exponent. If you put it on the quantity, it means to square the quantity, leaving the units alone. If you put it on the units, it means to square the units, leaving the quantity alone. If you want to square both, you have to use parentheses to extend the scope of the exponent: 25^2 m = (25*25) (m) 25 m^2 = (25) (m*m) (25 m)^2 = (25*25) (m*m) Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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