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Problems 1–7, 7B and 8–40 are concerned with arithmetic and elementary algebra. Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions.
Thus if expressed as a fraction with a numerator of 1, probability and odds differ by exactly 1 in the denominator: a probability of 1 in 100 (1/100 = 1%) is the same as odds of 1 to 99 (1/99 = 0.0101... = 0. 01), while odds of 1 to 100 (1/100 = 0.01) is the same as a probability of 1 in 101 (1/101 = 0.00990099... = 0. 0099). This is a minor ...
Using all numbers and all letters except I and O; the smallest base where 1 / 2 terminates and all of 1 / 2 to 1 / 18 have periods of 4 or shorter. 35 Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O.
This is a pure coincidence, as the metre was originally defined as 1 / 10 000 000 of the distance between the Earth's pole and equator along the surface at sea level, and the Earth's circumference just happens to be about 2/15 of a light-second. [40] It is also roughly equal to one foot per nanosecond (the actual number is 0.9836 ft/ns).
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2] Since the problem had withstood the attacks of ...
So are 1 and 2, 1 and 3, or 1 and 0.98. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors of ten). [2]
An increase of $0.15 on a price of $2.50 is an increase by a fraction of 0.15 / 2.50 = 0.06. Expressed as a percentage, this is a 6% increase. While many percentage values are between 0 and 100, there is no mathematical restriction and percentages may take on other values. [4]
((x),(y) = {239, 13 2} is a solution to the Pell equation x 2 − 2 y 2 = −1.) Formulae of this kind are known as Machin-like formulae . Machin's particular formula was used well into the computer era for calculating record numbers of digits of π , [ 39 ] but more recently other similar formulae have been used as well.
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