Chapter 6.4, Problem 33HP

To determine

To find: Calculated measurement and Actual measurement when percent error of calculation is $5\%$ .

Answer to Problem 33HP

When calculated measurement is $1.05$ times of Actual measurement then the percent error will be $5\%$ .

Explanation of Solution

Given information:

Percent error = $5\%$

Percent error $=\frac{A}{O}\times 100$

Where

  $A=$ Absolute value.

  $O=$ Actual value.

From given information

Percent error = $5\%$

Let us assume

Actual measurement as $\text{'}a\text{'}$

Calculated measurement as $\text{'}c\text{'}$

Absolute value = calculated value $-$ Actual value.

  $\Rightarrow A=c-a$

Therefore,

Percent error $=\frac{c-a}{a}\times 100$

  $\begin{array}{l}\Rightarrow 5=\frac{c-a}{a}\times 100\\ \Rightarrow \frac{5}{100}=\frac{c-a}{a}\\ \Rightarrow 0.05=\frac{c-a}{a}\\ \Rightarrow c-a=0.05a\\ \Rightarrow c=a+0.05a\\ \Rightarrow c=1.05a\end{array}$

Therefore

When calculated measurement is $1.05$ times of Actual measurement then the percent error will be $5\%$ .

Assume

Actual measurement = $100$

Calculated measurement = $105$

Then

Percent error = $\frac{105-100}{100}\times 100$

  $\Rightarrow$ Percent error = $\frac{5}{100}\times 100$

  $\Rightarrow$ Percent error = $5$