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If 10 is a primitive root modulo p, then the repetend length is equal to p − 1; if not, then the repetend length is a factor of p − 1. This result can be deduced from Fermat's little theorem, which states that 10 p−1 ≡ 1 (mod p). The base-10 digital root of the repetend of the reciprocal of any prime number greater than 5 is 9. [9]
Following the standard rules for representing numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, .... It can be proved that this number is 1; that is,
Thus, in the above example, after an increase and decrease of x = 10 percent, the final amount, $198, was 10% of 10%, or 1%, less than the initial amount of $200. The net change is the same for a decrease of x percent, followed by an increase of x percent; the final amount is p (1 - 0.01 x )(1 + 0.01 x ) = p (1 − (0.01 x ) 2 ) .
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
The part from the decimal separator to the right is the fractional part, which equals the difference between the numeral and its integer part. When the integral part of a numeral is zero, it may occur, typically in computing , that the integer part is not written (for example, .1234 , instead of 0.1234 ).
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Here, the base units are the quad, equal to 10 7 m (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to 10 −11 g, and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude. [36]: 268 [37]: 17
5 + 5 → 0, carry 1 (since 5 + 5 = 10 = 0 + (1 × 10 1) ) 7 + 9 → 6, carry 1 (since 7 + 9 = 16 = 6 + (1 × 10 1) ) This is known as carrying. When the result of an addition exceeds the value of a digit, the procedure is to "carry" the excess amount divided by the radix (that is, 10/10) to the left, adding it to the next positional value.