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The standard 12-hour clock and common use of 12 in English units emphasize the utility of the base. In addition, prior to its conversion to decimal, the old British currency Pound Sterling (GBP) partially used base-12; there were 12 pence (d) in a shilling (s), 20 shillings in a pound (£), and therefore 240 pence in a pound.
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Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8. Therefore, 59 + 27 = 86.
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base.In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten.
Common tools in early arithmetic education are number lines, addition and multiplication tables, counting blocks, and abacuses. [186] Later stages focus on a more abstract understanding and introduce the students to different types of numbers, such as negative numbers, fractions, real numbers, and complex numbers.
The base case b = 0 follows immediately from the identity element property (0 is an additive identity), which has been proved above: a + 0 = a = 0 + a. Next we will prove the base case b = 1, that 1 commutes with everything, i.e. for all natural numbers a, we have a + 1 = 1 + a.
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Another use of the base is to show the silver ratio as its representation in base √ 2 is simply 11 √ 2. In addition, the area of a regular octagon with side length 1 √ 2 is 1100 √ 2, the area of a regular octagon with side length 10 √ 2 is 110000 √ 2, the area of a regular octagon with side length 100 √ 2 is 11000000 √ 2, etc…
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