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NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Squared Decimals are Smaller 
Name: TJ
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: 9/13/2005
Question:
How can I explain logic behind when squaring decimals the product is lower. Example: 0.50 squared is 0.25.


Replies:
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[6363]... the sequence [6363] 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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