Editing Order of magnitude (section)

===Order-of-magnitude estimate===
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate [[Rounding|rounded]] to the nearest power of ten.  For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human [[population]] of the [[Earth]]) is 10 [[1000000000 (number)|billion]]. To round a number to its nearest order of magnitude, one rounds its logarithm to the nearest integer.  Thus {{val|4000000}}, which has a logarithm (in base 10) of 6.602, has 7 as its nearest order of magnitude, because "nearest" implies rounding rather than truncation.  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 {{val|1.7|e=8}} is 8, whereas the nearest order of magnitude for {{val|3.7|e=8}} is 9. An order-of-magnitude estimate is sometimes also called a [[zeroth order approximation]].