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Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number x to a power of some positive number b other than 1, are:
Prices are rounded down to the nearest multiple of 5 cents for sales ending in 1¢ & 2¢ (rounded to 0¢) and 6¢ & 7¢ (rounded to 5¢). Prices are rounded up to the nearest multiple of 5 cents for sales ending in 3¢ & 4¢ (round to 5¢) and 8¢ & 9¢ (round to 10¢). Values ending in 0¢ or 5¢ remain unchanged.
For example, to say that 14 × 15 was 201 would be unreasonable. Since 15 is a multiple of 5, the product should be as well. Likewise, 14 is a multiple of 2, so the product should be even. Furthermore, any number which is a multiple of both 5 and 2 is necessarily a multiple of 10, and in the decimal system would end with a 0. The correct answer ...
Round-to-nearest: () is set to the nearest floating-point number to . When there is a tie, the floating-point number whose last stored digit is even (also, the last digit, in binary form, is equal to 0) is used. For IEEE standard where the base is , this means when there is a tie it is rounded so that the last digit is equal to .
For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten (about 3.162). For example, the nearest order of magnitude for 1.7 × 10 8 is 8, whereas the nearest order of magnitude for 3.7 × 10 8 is 9. An order-of-magnitude ...
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The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
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