Final answer:
The greatest possible error of the measuring tape over 6 cm is not directly stated, as it typically relates to the precision of the device or the smallest division. The percent uncertainty of the tape over its entire length of 20 m is 0.025%. Percent error calculation requires an accepted value for comparison, which isn't given in this context.
Step-by-step explanation:
To determine the greatest possible error of the measuring tape mentioned, we must look at the data provided: a maximum deviation of 0.50 cm over 20 meters (2000 cm). This means the greatest possible error for a measurement of 6 cm would proportionally be (0.50 cm / 2000 cm) × 6 cm. However, since the error is described over a larger distance (20 m), using this maximum over smaller distances like 6 cm isn't practical in real-world scenarios. Typically, the device's precision or the smallest division on the measuring tool determines the greatest possible error for small distances.
To calculate the percent uncertainty of the measuring tape over the full 20 meters, we use the formula: Percent Uncertainty = (Greatest Possible Error / Measurement) × 100%, which yields (0.50 cm / 2000 cm) × 100% = 0.025%. Similarly, the percent error would require a comparison to a known or accepted value, which isn't provided in this context. When an accepted value is known, the percent error is calculated using the formula: Percent Error = |(Experimental Value - Accepted Value) / Accepted Value| × 100%. For the example given where the result is rounded to two significant figures (4.1 cm²), if an accepted value were provided, the percent error could then be calculated.