/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 A year is very nearly \(\pi \tim... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 22

A year is very nearly \(\pi \times 10^{7}\) s. By what percentage is this figure in error?

Short Answer

Expert verified
The percentage error when a year is estimated as \(\pi \times 10^{7}\) seconds is approximately 0.45%.

Step by step solution

01

Calculate the Actual Length of a Year in Seconds

First, calculate the actual length of a year in seconds. A year is composed of 365.25 days. Each day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds. Thus, the total is \(365.25 \times 24 \times 60 \times 60 = 3.15576 \times 10^{7}\) seconds.
02

Calculate the Estimated Length of a Year in Seconds

The problem states that a year is estimated as \(\pi \times 10^{7}\) seconds. This simplifies to approximately \(3.14159 \times 10^{7}\) seconds.
03

Calculate the Absolute Error

The absolute error in estimation is the actual time minus the estimated time. Thus, the absolute error is \(3.15576 \times 10^{7} - 3.14159 \times 10^{7} = 0.01417 \times 10^{7}\) seconds.
04

Calculate the Percentage Error

The percentage error is the absolute error divided by the actual measurement, multiplied by 100. So, the percentage error is \(\frac{(0.01417 \times 10^{7})}{(3.15576 \times 10^{7})} \times 100 = 0.45\% \) approximately.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A hydrogen atom is about \(0.1 \mathrm{nm}\) in diameter. How many hydrogen atoms lined up side by side would make a line \(1 \mathrm{cm}\) long?

One m/s is how many km/h?

How would you determine the length of a curved line?

In nanoseconds, how long is the period of the cesium-133 radiation used to define the second?

You're asked to specify the length of an updated aircraft model for a sales brochure. The original plane was 41 m long; the new model has a \(3.6-\mathrm{cm}\) -long radio antenna added to its nose. What length do you put in the brochure?
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Work Energy and Power

Read Explanation

Electric Charge Field and Potential

Read Explanation

Electricity and Magnetism

Read Explanation

Electromagnetism

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.