Whole Number Comparison with DecimalsOrdering of whole numbers is learnt by comparison of 1, 2, 3 and then multi-digit decimal forms or representations. The digits 0 to 9 in ascending or increasing order are: 0, 1, 2, 3 ,4, 5 ,6 7, 8, 9 Counting with decimals gives polynomials a0 + a1101 + a2102 + a3103 + a4104 + a5105 + .... = a5a4a3a2a1a0 in which the coefficients , a5, a4, a3, a2, a0 are given by digits 0 to 9. If two whole numbers are being compared via their decimal representations two cases are possible. Example 1: Decimal Representation have different lengths: 4912 is greater that 956 as the leading digit in the first occupies the thousand column while the leading digit in the second occupies the hundreds column. Example 2: Decimal Representation have same lengths: 34589 is less than 56721 as the leading digit 3 is less than 5. Learning by Examples: In a mathematics classes over a few years, many examples would illustrate the comparison of whole numbers by their one, two, three and longer decimal representations. How to describe more clearly in words fail me at the present time. In an advanced mathematics courses, one might discuss Lexicographic Ordering: Comparison by Conversion Method:
The minimal conversion method for comparison implies the common (minimal) conversion method for subtraction.
by conversion, that is by writing 30000 as 29000 + 1000 gives 2 9 10 Here the 3 in the ten thousand position is crossed-out and replaced by
2, 9 and 10 in the top row to indicate the replacement or conversion
of 30000 by/to 29000 + 1000. Here position indicates place value.
Following the conversion, in each column, the rows to be added combined have
more ones, tens, hundreds and so 2 9 10 |
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