Chapter 1: Q52. (page 20)

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

Short Answer

Expert verified

These watches have a percentage accuracy of 99.9999746%.

Step by step solution

Step 1. Definition of absolute error

The absolute error refers to the difference in the observed value and the true value of a quantity.

Step 2. Given data and assumption

The maximum absolute error in measurement of 1 year, $Δ t = \pm 8 s$ .

Step 3. Writing the formula for percentage error

The formula for percentage error is written as

$percentage error = \frac{absolute error}{expected value} \times 100$ .

Step 4. Calculating the expected value

After 1 year, the expected value of measurement will be

$\begin{matrix} expected value = 1 \times 365 \times 24 \times 60 \times 60 \\ = 3, 15, 36, 000 s \end{matrix}$

Step 5. Calculating the percentage error

Substituting the values in the formula for percentage error,

$\begin{matrix} percentage error = \frac{Δ t}{3, 15, 36, 000} \times 100 \\ = \frac{\pm 8}{3, 15, 36, 000 s} \times 100 \\ = 2.54 \times 10^{- 5} % \end{matrix}$

Step 6. Calculating the percentage accuracy

Percentage accuracy can be written in terms of percentage error as

Percentage accuracy = 100 – percentage error.

Substituting the values in the above equation,

Percentage accuracy = 99.9999746%.

Thus, the percentage accuracy is 99.9999746%.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

Short Answer

Step by step solution

Step 1. Definition of absolute error

Step 2. Given data and assumption

Step 3. Writing the formula for percentage error

Step 4. Calculating the expected value

Step 5. Calculating the percentage error

Step 6. Calculating the percentage accuracy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Kinematics Physics

Quantum Physics

Magnetism

Torque and Rotational Motion

Rotational Dynamics

Study anywhere. Anytime. Across all devices.