   # What is the uncertainty in the measured value 87.20030 after it is rounded to the following number of significant figures? a. 6 b. 5 c. 4 d. 2 ### General, Organic, and Biological C...

7th Edition
H. Stephen Stoker
Publisher: Cengage Learning
ISBN: 9781285853918

#### Solutions

Chapter
Section ### General, Organic, and Biological C...

7th Edition
H. Stephen Stoker
Publisher: Cengage Learning
ISBN: 9781285853918
Chapter 2, Problem 2.54EP
Textbook Problem
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## What is the uncertainty in the measured value 87.20030 after it is rounded to the following number of significant figures? a. 6 b. 5 c. 4 d. 2

(a)

Interpretation Introduction

Interpretation:

The uncertainty for the measured value 87.20030, when rounded off to 6 significant figures has to be identified.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures gives more information about the degree of uncertainty.  This uncertainty is determined from the last digit.  One should also note in which place the last digit appears, either in the tenth, or hundredth or thousandth place.

### Explanation of Solution

The location of the last significant figure of a measurement shows the uncertainty.  When the measured value 87.20030 is rounded off for the 6 significant figures, the value becomes 87.2003, the position of the last significant figure gives the uncertainty of the measurement, so the last significant figure here is 3, that is in ten thousandths place, Hence the uncertainty 0.0001.

Significantfigure=687

(b)

Interpretation Introduction

Interpretation:

The uncertainty for the measured value 87.20030, when rounded off to 5 significant figures has to be identified.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures gives more information about the degree of uncertainty.  This uncertainty is determined from the last digit.  One should also note in which place the last digit appears, either in the tenth, or hundredth or thousandth place.

(c)

Interpretation Introduction

Interpretation:

The uncertainty for the measured value 87.20030, when rounded off to 4 significant figures has to be identified.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures gives more information about the degree of uncertainty.  This uncertainty is determined from the last digit.  One should also note in which place the last digit appears, either in the tenth, or hundredth or thousandth place.

(d)

Interpretation Introduction

Interpretation:

The uncertainty for the measured value 87.20030, when rounded off to 2 significant figures has to be identified.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures gives more information about the degree of uncertainty.  This uncertainty is determined from the last digit.  One should also note in which place the last digit appears, either in the tenth, or hundredth or thousandth place.

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