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Equation 4 · Part 12 · Comparing the Main Approaches to Scientific Instruments and Metrology

superscript

uc2(y)=∑i=1N(∂f∂xi)2u2(xi)u_c^2(y) = \sum_{i=1}^{N} \left( \frac{\partial f}{\partial x_i} \right)^2 u^2(x_i)
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Uncertainty itself has a standard grammar, laid out in the GUM and adopted domestically by NIST in Technical Note 1297. Every source of doubt about a measured value is classified as either a Type A evaluation — estimated from the statistical scatter of repeated observations — or a Type B evaluation — estimated from any other information, such as a calibration certificate, a manufacturer’s specification, or physical reasoning about a known systematic effect [ 2 ] [ 3 ] . These component uncertainties are combined, following an explicit propagation rule, into a combined standard uncertainty, which is then multiplied by a coverage factor (conventionally k=2 , corresponding loosely to a 95%…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.