Questions: Which of the following measurement tools has greater measurement uncertainty: a meter stick that measures to the nearest centimeter (1 cm= 0.01 m) or a ruler that measures to the nearest millimeter (1 mm=0.001 m)? a meter stick b ruler c need more information

Which of the following measurement tools has greater measurement uncertainty: a meter stick that measures to the nearest centimeter (1 cm= 0.01 m) or a ruler that measures to the nearest millimeter (1 mm=0.001 m)?
a meter stick
b ruler
c need more information

Transcript text: Which of the following measurement tools has greater measurement uncertainty: a meter stick that measures to the nearest centimeter ( $1 \mathrm{~cm}=$ 0.01 m ) or a ruler that measures to the nearest millimeter $(1 \mathrm{~mm}=0.001 \mathrm{~m}) ?$ a meter stick b ruler c need more information

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine which measurement tool has greater measurement uncertainty: a meter stick that measures to the nearest centimeter or a ruler that measures to the nearest millimeter.

Step 2: Define Measurement Uncertainty

Measurement uncertainty refers to the range within which the true value is expected to lie. It is typically half of the smallest division of the measuring tool.

Step 3: Calculate Uncertainty for Each Tool

For the meter stick: The smallest division is 1 cm, so the uncertainty is $ \pm 0.5 $ cm or $ \pm 0.005 $ m.
For the ruler: The smallest division is 1 mm, so the uncertainty is $ \pm 0.5 $ mm or $ \pm 0.0005 $ m.

Step 4: Compare the Uncertainties