Chapter 1, Problem 5P

To determine

The percent uncertainty for the given measurement.

Answer to Problem 5P

The percentage uncertainty in the measurement given as 1.57 m² is approximately 1%.

Explanation of Solution

Given:

The given measurement is,

$A=1.57\text{m}$

Formula used:

The percentage uncertainty in a measurement is given by:

  $ϵ=\frac{\Delta \text{A}}{\text{A}}\times \text{100}$

Where, delta A is the uncertainty or error in the measurement of A.

Calculation:

As the measurement A = 1.57 m² is given up to two decimal places, so consider the uncertainty (or error) in the measurement of A as 0.01 m².

  $\therefore \Delta \text{A}=0.01\text{m}$

  $\therefore ϵ=\frac{0.01{\text{m}}^2}{1.57{\text{m}}^2}\times 100=0.6369$

Now, as the uncertainty in A has only one significant digit, the percentage uncertainty must also have only one significant digit. So round off the answer to one significant digit.

  $ϵ=0.6\%$

   $\approx 1\%$

Conclusion:

The percentage uncertainty in the measurement given as 1.57 m² is approximately 1 %.