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I'd like to describe measured temperature readings from a list, say 184, 185, 181, 187, as "Oil sump temperatures measured in the 180s°F during the start of the test." but I'm not sure if this is correct. Must I describe the range instead, as "between 180 and 190 degrees Fahrenheit"?

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How about

At the start of the test, the Oil sump temperatures were recorded in the range of 180°F-190°F

or

At the start of the test, the temperatures of the Oil sump were recorded in the range of 180°F-190°F

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Your example

180s°F

mixes two conventions in a creative way. I'll explain why you should avoid the usage.

The first convention is how one can refer to a specific decade or increment of tens. For instance, an abbreviated way of saying "the Seventies" might be:

The '70s saw the beginning of my favorite film franchise, Star Wars.

In this example, the '70s is a plural form combining every year from --70 to --79, as the APA Style Blog points out. Colloquially, temperatures are also referred to in ranges of ten, as when an imprecise weather prediction is given, and they take their form (e.g. low 40s) for a similar reason ("low 40s" describes multiple numbers in the lower part of the range between 40 and 49).

The second convention is how we describe temperature, which is fine in technical writing: 180°F, with the degree symbol and the letter for the measurement type nestled with the number without any spaces.

Why do these conventions not touch? First, most times when temperature is described as a range ("The high will be in the mid-70s"), it is described that way in a non-technical context where the temperature measure is clear and so no °F or °C is necessary. (An American audience would clearly understand that to be Fahrenheit; meteorologists usually speak or write to regional audiences.) Second, mixing the "s" and the "°F" could lead to the "s" being confused for a variable or parameter. Third, even if the risk of reader error is small, other expressions sound more precise with little loss of conciseness.

For those reasons I recommend writing in a way that is clear about the range. For instance:

Oil sump temperatures between 181°F and 187°F were measured during the start of the test."

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