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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144." [6]
If the multiplicand is a natural number then multiplication is the same as repeated addition, as in = + +. [52] Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor.
The numbers being multiplied are multiplicands, multipliers, or factors. Multiplication can be expressed as "five times three equals fifteen," "five times three is fifteen," or "fifteen is the product of five and three." Multiplication is represented using the multiplication sign (×), the asterisk (*), parentheses (), or a dot (⋅).
For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4. Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1. Several mathematical concepts expand upon the fundamental idea of multiplication.
Multiply both sides by the power of 10 just great enough (in this case 10 4) to move the decimal point just before the repeating part of the decimal number: 10,000x = 1,523. 987; Multiply both sides by the power of 10 (in this case 10 3) that is the same as the number of places that repeat: 10,000,000x = 1,523,987. 987
Wall Street closed Thursday in about the same shape, with the blue-chip Dow managing to eke out a small gain to snap a 10-day losing streak, the longest in 50 years.
Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude.
However, the equality of two real numbers given by an expression is known to be undecidable (specifically, real numbers defined by expressions involving the integers, the basic arithmetic operations, the logarithm and the exponential function). In other words, there cannot exist any algorithm for deciding such an equality (see Richardson's theorem