Editing Rounding (section)

===Logarithmic rounding===
====Rounding to a specified power====
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 {{mvar|x}} to a power of some positive number {{mvar|b}} other than 1, are:
:<math>\mathrm{roundToPower}(x, b) = b^{\mathrm{round}(\log_b x)}, x>0, b>0, b \ne 1</math>

Many of the caveats applicable to rounding to a multiple are applicable to rounding to a power.

====Scaled rounding====
This type of rounding, which is also named '''rounding to a logarithmic scale''', is a variant of [[#Rounding to a specified power|rounding to a specified power]]. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale.

For example, resistors are supplied with [[preferred number]]s on a logarithmic scale. In particular, for resistors with a 10% accuracy, they are supplied with nominal values 100, 120, 150, 180, 220, etc. rounded to multiples of 10 ([[E12 series]]). If a calculation indicates a resistor of 165 ohms is required then {{math|1=log(150) = 2.176}}, {{math|1=log(165) = 2.217}} and {{math|1=log(180) = 2.255}}. The logarithm of 165 is closer to the logarithm of 180 therefore a 180 ohm resistor would be the first choice if there are no other considerations.

Whether a value {{math|''x'' ∈ (''a'', ''b'')}} rounds to {{mvar|a}} or {{mvar|b}} depends upon whether the squared value {{math|''x''{{sup|2}}}} is greater than or less than the product {{math|''ab''}}. The value 165 rounds to 180 in the resistors example because {{math|1=165{{sup|2}} = 27225}} is greater than {{math|1=150 × 180 = 27000}}.