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To change 1 / 3 to a decimal, divide 1.000... by 3 (" 3 into 1.000... "), and stop when the desired accuracy is obtained, e.g., at 4 decimals with 0.3333. The fraction 1 / 4 can be written exactly with two decimal digits, while the fraction 1 / 3 cannot be written exactly as a decimal with a finite number of digits.
For example, in duodecimal, 1 / 2 = 0.6, 1 / 3 = 0.4, 1 / 4 = 0.3 and 1 / 6 = 0.2 all terminate; 1 / 5 = 0. 2497 repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; 1 / 7 = 0. 186A35 has period 6 in duodecimal, just as it does in decimal. If b is an integer base ...
An example is 3 tetrated to 4 is 3^3^3^3. ... The values containing a decimal point are approximate. ... over real x > −2 that satisfies
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".
A straightforward decimal rank system with a word for each order (10 十, 100 百, 1000 千, 10,000 万), and in which 11 is expressed as ten-one and 23 as two-ten-three, and 89,345 is expressed as 8 (ten thousands) 万 9 (thousand) 千 3 (hundred) 百 4 (tens) 十 5 is found in Chinese, and in Vietnamese with a few irregularities.
Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, [1] [2] [3] with the aforementioned generic terms reserved for abstract usage. [4] [5]
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For instance, if the number π is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to π than 3.141. [107] These methods allow computers to efficiently perform approximate calculations on real numbers.