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If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12. More generally, when casting out nines by summing digits, any set of digits which add up to 9, or a multiple of 9, can be ignored. In the number 3264, for example, the digits 3 and 6 sum to 9.
In mathematics, a multiple is the product of any quantity and an integer. [1] In other words, for the quantities a and b, it can be said that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that / is an integer.
9 is the fourth composite number, and the first odd composite number. 9 is also a refactorable number. [ 2 ] Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers in decimal , a method known as long ago as the 12th century.
For example, 90% would be described as "one nine"; 99% as "two nines"; 99.9% as "three nines"; and so forth. However, there are different conventions for representing inexact multiples of 9. For example, a percentage of 99.5% could be expressed as "two nines five" (2N5, or N2.5) [ 2 ] or as 2.3 nines, [ citation needed ] following from the ...
Larger multiples of the second such as kiloseconds and megaseconds are occasionally encountered in scientific contexts, but are seldom used in common parlance. For long-scale scientific work, particularly in astronomy, the Julian year or annum (a) is a standardised variant of the year, equal to exactly 31 557 600 seconds (365 + 1 / 4 days).
1098 = multiple of 9 containing digit 9 in its base-10 representation [92] ... 1455 = k such that geometric mean of phi(k) and sigma(k) is an integer [296]
Cycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypad. Figure 1 is used for multiples of 1, 3, 7, and 9. Figure 2 is used for the multiples of 2, 4, 6, and 8. These patterns can be used to memorize the multiples of any number from 0 to 10, except 5.
A sequence of six consecutive nines occurs in the decimal representation of the number pi (π), starting at the 762nd decimal place. [1] [2] It has become famous because of the mathematical coincidence, and because of the idea that one could memorize the digits of π up to that point, and then suggest that π is rational.