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Here the 'IEEE 754 double value' resulting of the 15 bit figure is 3.330560653658221E-15, which is rounded by Excel for the 'user interface' to 15 digits 3.33056065365822E-15, and then displayed with 30 decimals digits gets one 'fake zero' added, thus the 'binary' and 'decimal' values in the sample are identical only in display, the values ...
where a 1 = 0.0705230784, a 2 = 0.0422820123, a 3 = 0.0092705272, a 4 = 0.0001520143, a 5 = 0.0002765672, a 6 = 0.0000430638 erf x ≈ 1 − ( a 1 t + a 2 t 2 + ⋯ + a 5 t 5 ) e − x 2 , t = 1 1 + p x {\displaystyle \operatorname {erf} x\approx 1-\left(a_{1}t+a_{2}t^{2}+\cdots +a_{5}t^{5}\right)e^{-x^{2}},\quad t={\frac {1}{1+px ...
This rounding rule is biased because it always moves the result toward zero. Round-to-nearest: () is set to the nearest floating-point number to . When there is a tie, the floating-point number whose last stored digit is even (also, the last digit, in binary form, is equal to 0) is used.
If the n + 1 digit is greater than 5 or is 5 followed by other non-zero digits, add 1 to the n digit. For example, if we want to round 1.2459 to 3 significant figures, then this step results in 1.25. If the n + 1 digit is 5 not followed by other digits or followed by only zeros, then rounding requires a tie-breaking rule. For example, to round ...
Solution. Using Figure 3 and knowledge of the upstream and downstream conditions and the depth values on either side of the gate, a general estimate of the profiles upstream and downstream of the gate can be generated. Upstream, the water surface must rise from a normal depth of 0.97 m to 9.21 m at the gate.
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Suppose we have a continuous differential equation ′ = (,), =, and we wish to compute an approximation of the true solution () at discrete time steps ,, …,.For simplicity, assume the time steps are equally spaced: