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For example, "five tenths," is typically a measurement or tolerance of five ten-thousandths of an inch, and written as 0.0005 inches. "Three tenths," as another example, is written as 0.0003 inches [9] Machining "to within a few tenths" is often considered very accurate, and at or near the extreme limit of tolerance capability in most contexts.
1.5 × 10 −157 is approximately equal to the probability that in a randomly selected group of 365 people, all of them will have different birthdays. [ 3 ] 1 × 10 −101 is equal to the smallest non-zero value that can be represented by a single-precision IEEE decimal floating-point value.
In the mid-1960s, to defeat the advantage of the recently introduced computers for the then popular rally racing in the Midwest, competition lag times in a few events were given in centids (1 ⁄ 100 day, 864 seconds, 14.4 minutes), millids (1 ⁄ 1,000 day, 86.4 seconds), and centims (1 ⁄ 100 minute, 0.6 seconds) the latter two looking and ...
The omer, which the Torah mentions as being equal to one-tenth of an ephah, [30] is equivalent to the capacity of 43.2 eggs, or what is also known as one-tenth of three seahs. [31] In dry weight, the omer weighed between 1.560 kg to 1.770 kg, being the quantity of flour required to separate therefrom the dough offering . [ 32 ]
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
A floating-point number is a rational number, because it can be represented as one integer divided by another; for example 1.45 × 10 3 is (145/100)×1000 or 145,000 /100. The base determines the fractions that can be represented; for instance, 1/5 cannot be represented exactly as a floating-point number using a binary base, but 1/5 can be ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1. [12] There are many ways to see that, at least for absolute values | x | < 1, Euler is right in that + + = (+).
A polynomial P(x) has only finitely many perfect powers for all integers x if P has at least three simple zeros. [18] A generalization of Tijdeman's theorem concerning the number of solutions of y m = x n + k (Tijdeman's theorem answers the case k = 1), and Pillai's conjecture (1931) concerning the number of solutions of Ay m = Bx n + k.