Archived Vernier Caliper & Micrometer: Mr.Randall's Sig Fig Advice

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For measurements using a vernier caliper, lengths smaller than 1 cm should have at least two significant figures, while lengths between 1 cm and 9.99 cm should have three significant figures. The uncertain digit is represented by the Vernier scale digit, although guessing at the 1000th digit is rarely necessary. In contrast, a micrometer caliper allows for more precise measurements, enabling readings at the 0.001 mm level. This distinction is important for accurate reporting in lab work. The advice provided aims to clarify significant figure usage for better precision in measurements.
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I asked Mr. Randall about sig figs for this lab, especially on instruments like the vernier caliper and micrometer. This was his answer:

"For lengths smaller than 1 cm, you should get at least 2 sigs: 0.??. (To the 100th place, 0.01.)

Between 1 cm and 9.99 cm, you should get 3: ?.??

The Vernier scale digit takes the place of your “uncertain” digit. I’ve read articles that suggest if the Vernier scale line manages to fall between marks, readers are allowed to guess the 1000th digit, but I’ve never noticed that situation on a scale so small. I’m not expecting any values below the 0.01 place.

But the micrometer caliper scale can give you guessing capability at the 0.001 mm level, so 1.23 cm on a Vernier scale might read as 12.345 mm on the micrometer caliper."

I hope this helps anyone struggling as I was!
 
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Thanks for posting this ... it's something I might add to the next lab manual revision. :)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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