FloatingPointNumbersandArithmetic

2 decimal digits prior to any arithm etic operation

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Unformatted text preview: n is actually equivalent to about 7.2 decimal digits). Prior to any arithm etic operation, convert all operands to the leading seven digits – r ounding if necessary. (The leading digit is the leftm ost non - zer o – w here it occurs has nothing to do with a decim al p oint.) Examples: 1. 123.456789 converts to 123.4568 (notice the rounding) 2. 123456789000 converts to 123456800000. 3 . 00000000123456749 converts to .000000001234567. T o sim ulate a single floating poi nt com putation do this: a. D o the operation exactly . b. T ake this result, leave the decimal point w here it is, but truncate (or round) all digits follow ing the leading 7. Examples: 1. 123.4567 + 9.876543 = 133.333243 (exactly ) and this is truncated to 133.3332 (same w ith r ounding) 2. 123.4567 - 9.876543 = 113.580157 (exactly) and this is truncated to 113.5801 or rounded to 113.5802 3. 123.4567 * 9.876543 = 1219.3254061881 (exactly) and this is truncated to 1219.325 (same w ith rounding) 4. 123.4567 / 9.876543 = 12.499991140624811.....
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This note was uploaded on 03/21/2014 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas.

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