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The number 12565, for instance, has digit sum 1+2+5+6+5 = 19, which, in turn, has digit sum 1+9=10, which, in its turn has digit sum 1+0=1, a single-digit number. The digital root of 12565 is therefore 1, and its computation has the effect of casting out (12565 - 1)/9 = 1396 lots of 9 from 12565.
Both these methods break up the subtraction as a process of one digit subtractions by place value. Starting with a least significant digit, a subtraction of the subtrahend: s j s j−1... s 1. from the minuend m k m k−1... m 1, where each s i and m i is a digit, proceeds by writing down m 1 − s 1, m 2 − s 2, and so forth, as long as s i ...
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.
If this number is truncated to 4 decimal places, the result is 3.141. Rounding is a similar process in which the last preserved digit is increased by one if the next digit is 5 or greater but remains the same if the next digit is less than 5, so that the rounded number is the best approximation of a given precision for the original number.
The positional decimal system is presently universally used in human writing. The base 1000 is also used (albeit not universally), by grouping the digits and considering a sequence of three decimal digits as a single digit. This is the meaning of the common notation 1,000,234,567 used for very large numbers.
The only two differences between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement). For a 10-digit wheel (N), the fixed outside wheel is numbered from 0 to 9 (N-1).
For quantities created from measured quantities via addition and subtraction, the last significant figure position (e.g., hundreds, tens, ones, tenths, hundredths, and so forth) in the calculated result should be the same as the leftmost or largest digit position among the last significant figures of the measured quantities in the calculation ...
Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which this is commonly taught: The ten is moved from the next digit left, leaving in this example 3 − 1 in the tens column.
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