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A rational number, which can be expressed as finite continued fraction in two ways, z = [a 0; a 1, ..., a k − 1, a k, 1] = [a 0; a 1, ..., a k − 1, a k + 1] = p k / q k will be one of the convergents for the continued fraction expansion of a number, if and only if the number is strictly between (see this proof)
Many other number sets are built from the natural numbers. For example, the integers are made by adding 0 and negative numbers. The rational numbers add fractions, and the real numbers add infinite decimals. Complex numbers add the square root of −1. This chain of extensions canonically embeds the natural numbers in the other number systems ...
Share of adults that are obese, 1975 to 2016. Obesity is common in the United States and is a major health issue associated with numerous diseases, specifically an increased risk of certain types of cancer, coronary artery disease, type 2 diabetes, stroke, and cardiovascular disease, as well as significant increases in early mortality and economic costs. [1]
Silicon makes up 27.2% of the Earth's crust by weight, second only to oxygen at 45.5%, with which it always is associated in nature. Further fractionation took place in the formation of the Earth by planetary differentiation: Earth's core, which makes up 31.5% of the mass of the Earth, has approximate composition Fe 25 Ni 2 Co 0.1 S
California (/ ˌ k æ l ɪ ˈ f ɔːr n j ə /) is a state in the Western Region of the United States that lies on the Pacific Coast.It borders Oregon to the north, Nevada and Arizona to the east, and shares an international border with the Mexican state of Baja California to the south.
The 2023 report states that two billion people (26% of the population) do not have access to drinking water and 3.6 billion (46%) lack access to safely managed sanitation. [226] People in urban areas (2.4 billion) will face water scarcity by 2050. [225] Water scarcity has been described as endemic, due to overconsumption and pollution. [227]
[2] Between 1901 and 2018, the average sea level rose by 15–25 cm (6–10 in), with an increase of 2.3 mm (0.091 in) per year since the 1970s. [3]: 1216 This was faster than the sea level had ever risen over at least the past 3,000 years. [3]: 1216 The rate accelerated to 4.62 mm (0.182 in)/yr for the decade 2013–2022. [4]
[7] [8] Since China's transition to a socialist market economy through controlled privatisation and deregulation, [9] [10] the country has seen its ranking increase from ninth in 1978, to second in 2010; China's economic growth accelerated during this period and its share of global nominal GDP surged from 2% in 1980 to 18% in 2021.