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Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha : "A number remains unchanged when divided by zero."
Thus 0.(9) 1 = 0.9, 0.(9) 2 = 0.99, 0.(9) 3 = 0.999, and so on. ... Ordinarily, this definition leads to the real numbers, but for a decimal fraction ...
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
A simple and efficient way to state acuity is by converting the fraction to a decimal: 6/6 then corresponds to an acuity (or a Visus) of 1.0 (see Expression below), while 6/3 corresponds to 2.0, which is often attained by well-corrected healthy young subjects with binocular vision.
Just as the same fraction can be written in more than one way, the same real number may have more than one decimal representation. For example, 0.999... , 1.0, 1.00, 1.000, ..., all represent the natural number 1.
Vulgar Fraction One Seventh 2150 8528 ⅑ 1 ⁄ 9: 0.111... Vulgar Fraction One Ninth 2151 8529 ⅒ 1 ⁄ 10: 0.1 Vulgar Fraction One Tenth 2152 8530 ⅓ 1 ⁄ 3: 0.333... Vulgar Fraction One Third 2153 8531 ⅔ 2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ⁄ 5: 0.4 Vulgar ...
If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16:9 ...
A handy chart of decimal-fraction equivalents, 0 to 1 by 64ths. Prints nicely as 11x17 in landscape orientation. Useful for machinists who work with inch-based measurements. Date: 24 October 2007: Source: Own work: Author: Three-quarter-ten
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