To 4 d.p. a number is \(9.9190 .\) State (a) the maximum possible value, (b) the minimum possible value of the original number.

Short Answer

Expert verified
Answer: The maximum possible value of the original number is 9.91905, and the minimum possible value is 9.91895.

Step by step solution

01

Determine the rounding error

Since the number is given to 4 decimal places, the maximum possible error due to rounding is half of the value at the 5th decimal place. Therefore, the maximum error due to rounding is \(\frac{0.0001}{2} = 0.00005.\)
02

Find the maximum possible value

To find the maximum possible value of the original number, we need to add the rounding error to the given number. Maximum value = 9.9190 + 0.00005 = 9.91905
03

Find the minimum possible value

To find the minimum possible value of the original number, we need to subtract the rounding error from the given number. Minimum value = 9.9190 - 0.00005 = 9.91895
04

Answer

(a) The maximum possible value of the original number is 9.91905. (b) The minimum possible value of the original number is 9.91895.

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 Vaia!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free