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A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
In mathematics, Midy's theorem, named after French mathematician E. Midy, [1] is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period (sequence A028416 in the OEIS). If the period of the decimal representation of a/p is 2n, so that
Let x = the repeating decimal: x = 0.1523 987; Multiply both sides by the power of 10 just great enough (in this case 10 4) to move the decimal point just before the repeating part of the decimal number: 10,000x = 1,523. 987; Multiply both sides by the power of 10 (in this case 10 3) that is the same as the number of places that repeat:
Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".
First, every nonzero number with a finite decimal notation (equivalently, endless trailing 0s) has a counterpart with trailing 9s. For example, 0.24999... equals 0.25, exactly as in the special case considered. These numbers are exactly the decimal fractions, and they are dense. [41] [9] Second, a comparable theorem applies in each radix or base.
How To Make My 3-Ingredient Smoked Salmon Dip. For 2 1/2 cups, or 6 to 8 servings, you’ll need: 8 ounces cream cheese, room temperature 4 to 6 ounces hot smoked salmon, flaked
26% Twitter Following Increase Murray Wins Wimbledon, On and Off the Court Andy Murray’s victory was 77 years in the making. He not only brought the trophy back to Britain, but also
Well, Google has the answer! The search engine just released its annual map of "uniquely searched" Christmas cookies by state, based on Google Trends data from December 10 though 17.
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