Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 9

(a) What is the length of the pencil in the following figure if the ruler reads in centimeters? How many significant figures are there in this measurement? (b) An automobile speedometer with circular scales reading both miles per hour and kilometers per hour is shown. What speed is indicated, in both units? How many significant figures are in the measurements? [Section 1.6]

Short Answer

Expert verified
To measure the length of the pencil, place the ruler alongside the pencil and read the length in centimeters (cm). The number of significant figures depends on the smallest increment on the ruler. For example, if measured to be 12.5 cm, there are three significant figures. To determine the speed indicated on the automobile speedometer, locate the needle pointing to the current speed in both mph and km/h. The number of significant figures depends on the smallest increment shown on the speedometer. For example, if marked with increments of 1 mph and 1 km/h, count the number of digits in both measurements, including any zeros in the middle and end, but excluding any leading zeros.

Step by step solution

01

Measuring Length in Centimeters

To measure the length of the pencil, you will need to place the ruler alongside the pencil and read the value that lines up with the end of the pencil. Make sure you start at the zero mark of the ruler. Record the length in centimeters (cm).
02

Identifying the Number of Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one uncertain digit. For a ruler that shows centimeters, it is essential to identify the smallest increment on the ruler. For example, if the ruler has markings for every millimeter (mm), then the last digit in the measurement will be uncertain by at most a millimeter. Count the number of digits in the measurement, including any zeros in the middle and end, but excluding any leading zeros. This will give you the total number of significant figures. For example, if the length of the pencil is measured to be 12.5 cm, there are three significant figures.
03

Reading the Automobile Speedometer

To determine the speed indicated on the automobile speedometer, locate the needle that points to the current speed in both miles per hour (mph) and kilometers per hour (km/h). Note the values where the needle is pointing in both units.
04

Identifying the Number of Significant Figures in Measurements from the Speedometer

Just like in the case of a ruler, the number of significant figures depends on the smallest increment shown on the speedometer. For example, if the speedometer is marked with increments of 1 mph and 1 km/h, then the last digit in your measurement will be uncertain by at most 1 unit. Count the number of digits in the measurements for both mph and km/h, including any zeros in the middle and end, but excluding any leading zeros. This will give you the total number of significant figures for each measurement.

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

A copper refinery produces a copper ingot weighing \(70 \mathrm{~kg}\). If the copper is drawn into wire whose diameter is \(7.50 \mathrm{~mm}\), how many meters of copper can be obtained from the ingot? The density of copper is \(8.94 \mathrm{~g} / \mathrm{cm}^{3}\). (Assume that the wire is a cylinder whose volume \(V=\pi r^{2} h,\) where \(r\) is its radius and \(h\) is its height or length.)

(a) To identify a liquid substance, a student determined its density, Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\). sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL}\) ) or toluene (density \(0.866 \mathrm{~g} / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires $45.0 \mathrm{~g}\( of ethylene glycol, a liquid whose density is \)1.114 \mathrm{~g} / \mathrm{mL}$. Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the (d) A cubic piece of metal accuracy of measurement needed? measures $5.00 \mathrm{~cm}\( on each edge. If the metal is nickel, whose density is \)8.90 \mathrm{~g} / \mathrm{cm}^{3}$, what is the mass of the cube?

Zirconia, an oxide of zirconium, is often used as an affordable diamond substitute. Just like diamond, it is a colorless crystal which sparkles under sunlight. Which of the following physical properties do you think would help in differentiating between diamond and Zirconia-melting point, density, or physical state?

What is the number of significant figures in each of the following measured quantities? (a) \(902.5 \mathrm{~kg}\), (b) \(3 \times 10^{-6} \mathrm{~m}\), (c) \(0.0096 \mathrm{~L}\), (d) \(2.94 \times 10^{3} \mathrm{~m}^{2}\) (e) \(92.03 \mathrm{~km}\) (f) \(782.234 \mathrm{~g}\).

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A \(25.0-\mathrm{mL}\) portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at \(15^{\circ} \mathrm{C}\) as $0.8787 \mathrm{~g} / \mathrm{mL}$. Is the calculated density in agreement with the tabulated value? (b) An experiment requires \(15.0 \mathrm{~g}\) of cyclohexane, whose density at \(25^{\circ} \mathrm{C}\) is $0.7781 \mathrm{~g} / \mathrm{mL}$. What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of \(5.0 \mathrm{~cm}\). What is the mass of the sphere if lead has a density of $11.34 \mathrm{~g} / \mathrm{cm}^{3} ?\( (The volume of a sphere is \)(4 / 3) \pi r^{3},\( where \)r$ is the radius.)
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Physical Chemistry

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