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And the other three binary-expansion repeating sequences give the 3-cycle 110110110... → 101101101... → 011011011... → 110110110.... Either of these 3-cycles can be converted to fraction form: for example, the first-given 3-cycle can be written as 1 / 7 → 2 / 7 → 4 / 7 → 1 / 7 .
The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 2 2 × 3) makes it easier to handle the common fractions of 1 ⁄ 3 and 1 ⁄ 4 than does a system based on ten (10 = 2 × 5).
4 Line feed is used for "end of line" in text files on Unix / Linux systems. 5 Carriage Return (accompanied by line feed) is used as "end of line" character by Windows, DOS, and most minicomputers other than Unix- / Linux-based systems 6 Control-O has been the "discard output" key. Output is not sent to the terminal, but discarded, until ...
In the figure, the fraction 1/9000 is displayed in Excel. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using ...
For example, the Environmental Protection Agency estimates that coal kills 30,000 people a year, [268] as a result of its environmental impact, while 60 people died in the Chernobyl disaster. [269] A real world example of impact provided by proponents is the 650,000 ton increase in carbon emissions in the two months following the closure of the ...
[4] [5] Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples increases.
Here are two examples of the questions asked: What is the highest grade (or year) of school this person has ever attended? Did he finish the highest grade (or year) he attended? The answers consisted mostly of the following: No school completed or never attended school; Nursery school (added as a choice in 1960)
Claude is a family of large language models developed by Anthropic. [1] [2] The first model was released in March 2023.The Claude 3 family, released in March 2024, consists of three models: Haiku, optimized for speed; Sonnet, which balances capability and performance; and Opus, designed for complex reasoning tasks.