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Equation 4 · Part 12 · The Last Artefact: Redefining the Kilogram

Numerator: 4

KJ=2eh,RK=he2,KJ2RK=4hK_{\mathrm J} = \frac{2e}{h}, \qquad R_{\mathrm K} = \frac{h}{e^{2}}, \qquad K_{\mathrm J}^{2} R_{\mathrm K} = \frac{4}{h}
44

What this part means

The complete quantity above the fraction bar.

Its job in the formula

4 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…resistance against the von Klitzing constant, taken as RK = h/e², so that KJ²RK = 4/h and the mass reduces to h multiplied by an experimental frequency term and divided by the product of local gravity and coil velocity [ 4 ] : KJ=2eh,RK=he2,KJ2RK=4hK_{\mathrm J} = \frac{2e}{h}, \qquad R_{\mathrm K} = \frac{h}{e^{2}}, \qquad K_{\mathrm J}^{2} R_{\mathrm K} = \frac{4}{h}. This is where the quantum electrical standards earn their place. Since 1990 the practical realization of the volt and the ohm had rested on the Josephson and quantum Hall effects, but with conventional values assigned to the two constants — a decision Taylor and Witt set…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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