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Chapter 2: Problem 166

Indicate whether the trailing zero in each value is significant, not significant, or possibly significant: (a) \(540 \pm 0.5\) (b) \(540 \pm 5\) (c) \(0.540\) (d) \(0.000540\) (e) 540

Short Answer

Expert verified
(a) Possibly significant, (b) Not significant, (c) Significant, (d) Significant, (e) Possibly significant

Step by step solution

01

(a) Determine the significance of trailing zero in \(540 \pm 0.5\)

In this case, the value is \(540 \pm 0.5\). The uncertainty given is \(\pm 0.5\), meaning the actual value could be between \(539.5\) and \(540.5\). Since we can't know whether the zero is required to hold its place, the trailing zero can be considered possibly significant.
02

(b) Determine the significance of trailing zero in \(540 \pm 5\)

For the value \(540 \pm 5\), the actual value could be between \(535\) and \(545\). In this case, the trailing zero is not significant, because it doesn't affect the range of uncertainty.
03

(c) Determine the significance of trailing zero in \(0.540\)

The value is given as \(0.540\). The decimal has been used to indicate precision, and thus the trailing zero is indeed significant, as it indicates there is a higher level of precision.
04

(d) Determine the significance of trailing zero in \(0.000540\)

For the given value of \(0.000540\), the trailing zero is also significant. Here, the zero is necessary to maintain the given level of precision.
05

(e) Determine the significance of trailing zero in 540

The value is given as 540, which doesn't have any decimal. In this case, the significance of the trailing zero is ambiguous without any other context. So, the trailing zero is possibly significant.

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