<x-tad-smaller>Hello. Could someone please tell me if a square meter is approx 10% larger than a square yd? I have heard that another rule of thumb is that a meter is approx 10 % longer than a yd.� A yd plus 10 % is 39.36 in. A meter is 10 % longer than a yd minus .23�of an inch.� Close enough for every day use.� ������</x-tad-smaller>
John,
The answer is "No, it is not 10% larger; it is 20% larger."
It a general rule that if one value is a certain percent larger than another, then the square of one will be TWICE that percentage larger than the square of the other.
This rule works well for all small percentages. Thus, if ANY two things are 10% different, their squares will be 20% different. The rule is especially good for very small percentages, but even as high as 10% it is still a pretty good approximation. (Also, the percent difference of the cubes is THREE times different, so a cubic metre is 30% larger than a cubic yard.)
But, if you don't believe it, you can always do the easy math to check it (see the P.S. below).
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
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Make it simple; Make it Metric
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P.S.
Here is the easy (though longer) calculation for the particular case of the square yard and square metre.
Use the fact that 1 yd = 0.91 m (which you may know, or you could easily look up or figure out from other known conversions like 2.54 cm - 1 inch). You could use 0.91440 m to be even more precise - but you're looking for a "rule of thumb" approximation here, so great precision is surely not important.
Square both sides of 1 yd = 0.91 m.
Left side is easy:
(1 yd) x (1 yd) which equals 1 yd^2 (one square yard)
Right side is also easy, if you use a calculator:
(0.91 m) x (0.91 m) which equals 0.83 m^2.
So the result is 1 yd^2 = 0.83 m^2 .
(The calculator will tell you it is 0.8281 but you should
know that if you calculate from numbers having only two
digits, your answer will usually have only two good
digits; any extra ones are meaningless.)
The value 0.83 m^2 is less than 1 m^2 (one square metre) by
0.17 m^2 , (1.00 m^2 - 0.83 m^2).
This is easy with a calculator and almost as easy without one.
That difference of 0.17 m^2 expressed as a per cent of the original
size of 0.83 m^2 is found by dividing 0.17/0.83 to get 0.20, and
shifting the decimal point two places yields the percentage which is
therefore 20%.
