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Len Over 21 wrote:
... NTSC color subcarrier is exactly 3.579545454545454545454545.... MHz. :-) With the correct integer divisor and correct integer multiplier, it comes out to 500 KHz fairly exact. "Fairly exact"? What's that mean? Any repeating decimal can be written as a rational number, a/b. That particular decimal above is exactly 315/88: Set that decimal equal to N. Since two digits repeat, multiply both sides of the equation by 10^2; we now have: 100N = 357.9545454... Next, subtract the first equation from this second one; all the repeating 54 pairs cancel due to this subtraction, giving us 99N = 354.375, a terminating decimal. To eliminate the decimal point, multiply both sides by 1000: 99000N = 354375. Now divide both sides by 99000: N = 354375/99000. This fraction simplifies to N = 315/88. Hence, that original repeating decimal, 3.579545454... is exactly equal to 315/88. Note that if you have a repeating decimal with 3 repeating digits, you'd multiple both sides of the initial equation by 10^3, etc. Jeff KH6O -- Chief Petty Officer, U.S. Coast Guard Mathematics Lecturer, University of Hawaii System |
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