Squared Decimals are Smaller
How can I explain logic behind when squaring decimals the
product is lower. Example: 0.50 squared is 0.25.
The logic of this result is the theorem from number theory (do not be
intimidated by the complicated-sounding phrase). "EVERY DECIMAL LESS THAN
ONE (0.abc...) IS EXACTLY EQUAL TO A RATIONAL NUMBER (p/q), AND EVERY
RATIONAL NUMBER (n/m) IS EXACTLY EQUAL TO A REPEATING DECIMAL SEQUENCE.
For example 0.5000... (the digit '0' repeats) = 1/2; 1/3 = 0.333... (the
digit '3'); 2/3 = 0.666...(the digit '6' repeats); 7/11= 0.6363...
the sequence  is the repeating decimal sequence. By the rules of
multiplication of rational numbers in fractional form: n/m *p/q =
(n*p)/(m*q) which must always be less than fraction because in each the
numbers in the numerators are smaller than the numbers in the denominator.
So clearly, the square of a fraction p/q < 1 means p
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Update: June 2012