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What does "to 1 part in 2x10^5" means in this sentence?

A bridge circuit enable us to measure the change in capacitance to 1 part in 2x10^5, equivalent to a rotation angle of 8x10^(-8) rad, with an integration time of 1s when the device is in a vacuum.

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    This question appears to be off-topic because it is about scientific notation, not English. – FumbleFingers Nov 17 '14 at 21:03
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    That's another way of saying "5 ppm" or "five parts per million" . . . – Robusto Nov 17 '14 at 21:09
  • It would be spoken as "one part in two times ten to the fifth" (or perhaps "... fifth power"). You may see several different notations for "to the Nth power" -- ^ as seen above, ** when written by old FORTRAN programmers, or with the N as superscript, when the typesetting system supports it. And likely several others that one would have to figure out from context. – Hot Licks Nov 18 '14 at 2:10
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The caret (^) is used in several programming languages (as well as many graphing calculators, TeX and Microsoft Excel macros) to indicate a power, and some engineers or developers will use this convention in ordinary prose. Exponentiation is usually represented with superscripts, but the correct orthography is sometimes difficult or impossible to produce. Thus, ^5 indicates to the fifth power, which would ordinarily be set as superscript 5 (x⁵).

More broadly, the amount is expressed in expressed in scientific notation, in which values are expressed as multiples of a power of ten. This system makes it easier to represent very large or very small numbers and for people to comprehend their magnitude— most people would need to take some time to figure out which is the greater of 0.0000000825943201 and 0.00000000473201, for example, or to determine that the latter number is equivalent to 473,201 hundred-trillionths.

Thus, 1 part in 2x10^5 is equivalent to 1 part in 2 × 10⁵ or 1 part in 200,000, or 0.000005 (or 0.0005% as IanF1 notes). By the same token, 8x10^(-8) rad is equivalent to 8×10⁻⁸ or 0.00000008 radians.

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It's short for "to an accuracy of 1 part in 2x10^5" ie an accuracy of 0.0005%.

2x10^5 is scientific notation for 200000.

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