What is the uncertainty for this measurement [Fill in the blank],
cm. The numbers shown on the tape are in cm. (Only add the numerical value here, do not add +/- or the units)

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Question

What is the uncertainty for this measurement [Fill in the blank],
cm. The numbers shown on the tape are in cm. (Only add the numerical value here, do not add +/- or the units)

Open this image in a new tab if your image does not load

BlackTom AI · Accepted Answer

To begin, I will restate the provided items before diving into the reasoning:
- Question: What is the uncertainty for this measurement [Fill in the blank], cm. The numbers shown on the tape are in cm. (Only add the numerical value here, do not add +/- or the units)
- Answer (given by the dataset): 0.1
- Answer options: not provided in this instance

Now, let's analyze how to determine uncertainty in a measurement using a ruler or tape with markings in centimeters.

- Step A: Understand the instrument’s smallest division. If the tape’s markings are in increments of 0.1 cm, then the finest scale you can read directly is 0.1 cm. Each block represents a tenth of a centimeter, which is the precision limit of the reading.
- Step B: Interpret the instruction about uncertainty. When a measurement is read to the nearest smallest division, a common convention is to assign an uncertainty that corresponds to that smallest division (or, in some cases, half of it). Here, since the instruction asks for the numerical uncertainty value and the smallest division is 0.1 cm, the reported uncertainty level aligns with this scale.
- Step C: Consider alternate conventions. Another typical approach is to take half of the smallest division as the uncertainty, which would be 0.05 cm if the smallest division is 0.1 cm. However, the dataset’s provided answer specifies 0.1, indicating the convention being used for this question.
- Step D: Address missing context about options. The prompt does not present multiple options to evaluate, so I will focus on why the given numeric value matches the common interpretation under the stated instruction and scale. The core idea is that the measurement’s precision is limited by the smallest visible marking, which here is 0.1 cm, so the uncertainty is tied to that scale.
- Step E: Summarize the reasoning. Since the tape is graduated in 0.1 cm increments, the uncertainty tied to a measurement read to the nearest 0.1 cm is typically expressed as 0.1 cm under the convention used in this question’s dataset. This aligns with the instruction to provide only the numerical value without signs or units.

If you encounter a different instrument with a smallest division of, say, 0.05 cm, you would adjust accordingly and consider whether the convention used in your course is to report the half-division as the uncertainty or the full division. In this particular case, the dataset indicates 0.1 as the uncertainty value, consistent with reading to the nearest 0.1 cm on a tape.

FFP001 Threshold Quiz 2 | LA007

What is the uncertainty for this measurement [Fill in the blank], cm. The numbers shown on the tape are in cm. (Only add the numerical value here, do not add +/- or the units) Open this image in a new tab if your image does not load

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