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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.
The earliest such device had a single logarithmic scale for performing multiplication and division, but soon an improved technique was developed which involved two such scales sliding alongside each other. Later, multiple scales were provided with the most basic being logarithmic but with others graduated according to the mathematical function ...
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.
[6]: Sec. 59, also p. 156 [4]: 16 Logarithms of sines for angles from 30 degrees to 90 degrees are then computed by finding the closest number in the radical table and its logarithm and calculating the logarithm of the desired sine by linear interpolation. He suggests several ways for computing logarithms for sines of angles less than 30 degrees.
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
Mathematical tables containing common logarithms (base-10) were extensively used in computations prior to the advent of computers and calculators, not only because logarithms convert problems of multiplication and division into much easier addition and subtraction problems, but also for an additional property that is unique to base-10 and ...
William Oughtred (5 March 1574 – 30 June 1660), [1] also Owtred, Uhtred, etc., was an English mathematician and Anglican clergyman. [2] [3] [4] After John Napier discovered logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, Oughtred was the first to use two such scales sliding by one another to perform direct multiplication and ...
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.