To determine the uncertainty of the value [tex]\( 4.60 \times 10^3 \)[/tex] fluid ounces, we need to consider the precision of the value presented. Precision is indicated by the number of significant figures or decimal places in the measurement.
The value given is [tex]\( 4.60 \times 10^3 \)[/tex] fluid ounces. The number [tex]\( 4.60 \)[/tex] has two decimal places, indicating a specific level of precision. To match this precision with an appropriate uncertainty, we must find the uncertainty that corresponds to the same level of decimal places.
Let's analyze the given options:
1. [tex]\( \pm 100 \)[/tex] fluid ounces: This uncertainty is suitable for measurements with no or fewer decimal places.
2. [tex]\( \pm 10 \)[/tex] fluid ounces: This uncertainty is still too coarse for our significant figures.
3. [tex]\( \pm 1 \)[/tex] fluid ounce: This is closer but still not precise enough.
4. [tex]\( \pm 0.1 \)[/tex] fluid ounce: This is getting closer but still not matching our level of decimal precision.
5. [tex]\( \pm 0.01 \)[/tex] fluid ounce: This uncertainty properly matches the precision level of two decimal places (as in [tex]\( 4.60 \)[/tex]).
Therefore, the correct uncertainty that matches the precision of [tex]\( 4.60 \times 10^3 \)[/tex] fluid ounces is [tex]\( \pm 0.01 \)[/tex] fluid ounce.
