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The rule to calculate significant figures for multiplication and division are not the same as the rule for addition and subtraction. For multiplication and division, only the total number of significant figures in each of the factors in the calculation matters; the digit position of the last significant figure in each factor is irrelevant.
Mannheim's rule had two major modifications that made it easier to use than previous general-purpose slide rules. Such rules had four basic scales, A, B, C, and D, and D was the only single-decade logarithmic scale; C had two decades, like A and B. Most operations were done on the A and B scales; D was only used for finding squares and square ...
The calculator's unusual single-scale design [note 3] makes its 12.70-metre (500-inch) helical spiral equivalent to a scale twice this length on a traditional slide rule – 25.40 metres (1,000 inches) long. The scale can always be read to four significant figures and often to five.
Following the patent and release of Harold's Long Scale calculator featuring two knobs on the outside rim in 1914, he designed the Magnum Long Scale calculator in 1927. [6] [7] As the name "Magnum" implies, it was a fairly large device at 4.5 inches in diameter—about 1.5 inches more than Fowler's average non-Magnum-series calculators. [8]
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform calculations using basic (addition, subtraction, multiplication, division) and advanced (trigonometric, hyperbolic, etc.) mathematical operations and functions.
The stepped reckoner or Leibniz calculator was a mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz (started in 1673, when he presented a wooden model to the Royal Society of London [2] and completed in 1694). [1]
Log tables, slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results. [ 3 ]