Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 17

Express each of the following to four significant digits: a) \(\frac{1}{3}\) b) \(89 \frac{2}{3}\) c) \(2300.71\) d) \(\frac{3}{1000} s\) e) \(\frac{1}{3000}\) f) \(\frac{9}{882}\)

Short Answer

Expert verified
Question: Express each of the following numbers to four significant digits: a) \(\frac{1}{3}\) b) \(89\frac{2}{3}\) c) \(2300.71\) d) \(\frac{3}{1000}s\) e) \(\frac{1}{3000}\) f) \(\frac{9}{882}\) Answer: a) \(0.3333\) b) \(89.67\) c) \(2300.7\) d) \(0.003s\) e) \(0.000333\) f) \(0.0102\)

Step by step solution

01

a) Convert \(\frac{1}{3}\) to decimal

Divide 1 by 3 to get the decimal representation of the fraction. \(\frac{1}{3} = 0.3333\overline{3}\)
02

a) Round to four significant digits

Round the decimal to four significant digits: \(0.3333\overline{3}\approx 0.3333\)
03

b) Convert \(89\frac{2}{3}\) to decimal

The mixed number \(89\frac{2}{3}\) can be converted to a decimal by dividing 2 by 3 and adding 89: \(89 + \frac{2}{3}\approx 89.6667\)
04

b) Round to four significant digits

Round the decimal to four significant digits: \(89.6667\approx 89.67\)
05

c) Round \(2300.71\) to four significant digits

\(2300.71\) is already in decimal form. To round it to four significant digits, we don't have to make any changes: \(2300.71 = 2300.7\)
06

d) Convert \(\frac{3}{1000}s\) to decimal equivalent

Divide 3 by 1000 to get the decimal representation of the fraction: \(\frac{3}{1000}s = 0.003s\)
07

d) Round to four significant digits

Since \(0.003s\) has only one non-zero digit and three leading zeros, no rounding is needed: \(0.003s\) has one significant digit and is already rounded.
08

e) Convert \(\frac{1}{3000}\) to decimal

Divide 1 by 3000 to get the decimal representation of the fraction: \(\frac{1}{3000}= 0.000\overline{3}\)
09

e) Round to four significant digits

Since \(0.000\overline{3}\) has only one non-zero digit and three leading zeros, round the number to four significant digits: \(0.000\overline{3}\approx 0.000333\)
10

f) Convert \(\frac{9}{882}\) to decimal

Divide 9 by 882 to get the decimal representation of the fraction: \(\frac{9}{882}\approx 0.0102\)
11

f) Round to four significant digits

Since \(0.0102\) has four non-zero digits, no further rounding is needed: \(0.0102\approx 0.0102\)

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!

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

Select the correct statement: a) The temperature is \(10^{\circ} \mathrm{K}\). b) The temperature is \(283^{\circ} \mathrm{C}\). c) The temperature is 10 kelvins. d) The temperature is 283 Celsius.

Write each of the following using base units without the use of a prefix: a) \(4 \times 10^{-6} \mathrm{GF} / \mathrm{m}\) b) \(65.2 \mathrm{fF} / \mathrm{m}\) c) \(0.00347 \mathrm{pPa} / \mathrm{kg}\)

Round off \(6743.865\) to: a) six significant digits b) five significant digits c) four significant digits d) three significant digits e) two significant digits

Write each of the following in a correct form without using any exponents: a) \(12300 \mathrm{Nm} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\) b) \(109.433 \mathrm{Cs} \mathrm{m}^{-1} \mathrm{~K}^{-1}\) c) \(0.000433 \mathrm{~W} \mathrm{~s} \mathrm{~m}^{-3} \mathrm{~K}^{-1}\)

Write each of the following using base units only, and without the use of a prefix: a) \(5643 \mathrm{kN} / \mathrm{t}\).d b) \(453000 \mu \mathrm{H} /(\mathrm{kg} \cdot \mathrm{h})\) c) \(654.0004 \mathrm{nS.m} /(\mathrm{h} . \mathrm{kg})\)
See all solutions

Recommended explanations on Physics Textbooks

Space Physics

Read Explanation

Medical Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Particle Model of Matter

Read Explanation

Nuclear Physics

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.

Sign-up for free