General, Organic, and Biological Chemistry
General, Organic, and Biological Chemistry
7th Edition
ISBN: 9781285853918
Author: H. Stephen Stoker
Publisher: Cengage Learning
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Chapter 2, Problem 2.66EP

(a)

Interpretation Introduction

Interpretation:

Answer for (4.0x104)x(1.32x108) has to be expressed in scientific notation with the correct number of significant figures.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “A x 10n, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

For multiplication of the scientific notation, the coefficients are multiplied as such and the exponents are added.  For division of the scientific notation, the coefficients are divided as such and the exponents are subtracted.

(a)

Expert Solution
Check Mark

Answer to Problem 2.66EP

Answer for (4.0x104)x(1.32x108) is 5.3x1012.

Explanation of Solution

Given scientific notation is (4.0x104)x(1.32x108).

The coefficient has to be multiplied and the exponents has to be added.  This can be done as shown below,

  (4.0x104)x(1.32x108) = 5.28x104+8 = 5.28x1012

This value has to be expressed to the correct number of significant figures.  One of the number that is multiplied has three significant figures while the other has two significant figures.  Hence, the answer is expressed with two significant figures as 5.3x1012.

(b)

Interpretation Introduction

Interpretation:

Answer for (3.200x107)x(1.10x10-2)x(2.3x10-7) has to be expressed in scientific notation with the correct number of significant figures.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “A x 10n, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

For multiplication of the scientific notation, the coefficients are multiplied as such and the exponents are added.  For division of the scientific notation, the coefficients are divided as such and the exponents are subtracted.

(b)

Expert Solution
Check Mark

Answer to Problem 2.66EP

Answer for (3.200x107)x(1.10x10-2)x(2.3x10-7) is 8.1x10-2.

Explanation of Solution

Given scientific notation is (3.200x107)x(1.10x10-2)x(2.3x10-7).

The coefficient has to be multiplied and the exponents has to be added.  This can be done as shown below,

  (3.200x107)x(1.10x10-2)x(2.3x10-7) = 8.096x107-2-7 = 8.096x102

This value has to be expressed to the correct number of significant figures.  One of the number that is multiplied has two significant figures.  Hence, the answer is expressed with two significant figures as 8.1x102.

(c)

Interpretation Introduction

Interpretation:

Answer for (6.0x10-5)÷(3.0x103) has to be expressed in scientific notation with the correct number of significant figures.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “A x 10n, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

For multiplication of the scientific notation, the coefficients are multiplied as such and the exponents are added.  For division of the scientific notation, the coefficients are divided as such and the exponents are subtracted.

(c)

Expert Solution
Check Mark

Answer to Problem 2.66EP

Answer for (6.0x10-5)÷(3.0x103) is 2.0x10-8.

Explanation of Solution

Given scientific notation is (6.0x10-5)÷(3.0x103).

The coefficient has to be divided and the exponents has to be subtracted.  This can be done as shown below,

  (6.0x10-5)÷(3.0x103) = 2.0x10-5-3 = 2.0x108

This value has to be expressed to the correct number of significant figures.  Both the scientific notation has got two significant figures.  Hence, the answer is expressed with two significant figures as 2.0x108.

(d)

Interpretation Introduction

Interpretation:

Answer for (3.2x102)x(3.31x106)/(4.00x10-3)x(2.0x106) has to be expressed in scientific notation with the correct number of significant figures.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “A x 10n, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

For multiplication of the scientific notation, the coefficients are multiplied as such and the exponents are added.  For division of the scientific notation, the coefficients are divided as such and the exponents are subtracted.

(d)

Expert Solution
Check Mark

Answer to Problem 2.66EP

Answer for (3.2x102)x(3.31x106)/(4.00x10-3)x(2.0x106) is 1.3x105.

Explanation of Solution

Given scientific notation is (3.2x102)x(3.31x106)/(4.00x10-3)x(2.0x106).

For multiplication, the coefficient has to be multiplied and the exponent has to be added and for division the coefficient has to be divided and the exponents has to be subtracted.  This can be done as shown below,

  (3.2x102)x(3.31x106)/(4.00x10-3)x(2.0x106) = (10.592x102+6)÷(8.00x10-3+6) = (10.592x108)÷(8.00x103) = 1.324x108-3 = 1.324x105

This value has to be expressed to the correct number of significant figures.  In scientific notations the least number of significant figure present is two.  Hence, the answer is expressed with two significant figures as 1.3x105.

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Chapter 2 Solutions

General, Organic, and Biological Chemistry

Ch. 2.3 - Prob. 2QQCh. 2.4 - Prob. 1QQCh. 2.4 - Prob. 2QQCh. 2.4 - Prob. 3QQCh. 2.4 - Prob. 4QQCh. 2.4 - Prob. 5QQCh. 2.4 - Prob. 6QQCh. 2.5 - In which of the following cases is the given...Ch. 2.5 - When rounded to three significant figures, the...Ch. 2.5 - Prob. 3QQCh. 2.5 - Prob. 4QQCh. 2.6 - Prob. 1QQCh. 2.6 - Prob. 2QQCh. 2.6 - Prob. 3QQCh. 2.6 - Prob. 4QQCh. 2.6 - Prob. 5QQCh. 2.6 - Prob. 6QQCh. 2.7 - Prob. 1QQCh. 2.7 - Prob. 2QQCh. 2.7 - Which of the following is an incorrect conversion...Ch. 2.7 - Prob. 4QQCh. 2.8 - Prob. 1QQCh. 2.8 - Prob. 2QQCh. 2.9 - Prob. 1QQCh. 2.9 - Prob. 2QQCh. 2.9 - Prob. 3QQCh. 2.9 - What is the mass, in grams, of 30.0 mL of liquid...Ch. 2.10 - The freezing point of water is a. 0F b. 0 K c. 0C...Ch. 2.10 - Prob. 2QQCh. 2.10 - Prob. 3QQCh. 2.10 - Prob. 4QQCh. 2 - What is the main reason scientists prefer to use...Ch. 2 - List the more common types of measurements made in...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Arrange each of the following from smallest to...Ch. 2 - Arrange each of the following from smallest to...Ch. 2 - Which of the two given units is the more logical...Ch. 2 - Which of the two given units is the more logical...Ch. 2 - A person is told that there are 60 minutes in an...Ch. 2 - Prob. 2.12EPCh. 2 - Indicate whether the number in each of the...Ch. 2 - Indicate whether the number in each of the...Ch. 2 - Indicate whether each of the following quantities...Ch. 2 - Indicate whether each of the following quantities...Ch. 2 - Identify the estimated digit in each of the...Ch. 2 - Identify the estimated digit in each of the...Ch. 2 - Prob. 2.19EPCh. 2 - Prob. 2.20EPCh. 2 - Indicate to what decimal position readings should...Ch. 2 - Indicate to what decimal position readings should...Ch. 2 - Consider the following rulers as instruments for...Ch. 2 - Consider the following rulers as instruments for...Ch. 2 - Using the rulers given in Problem 2-23, what is...Ch. 2 - Using the rulers given in Problem 2-23, what is...Ch. 2 - With which of the rulers in Problem 2-23 was each...Ch. 2 - With which of the rulers in Problem 2-23 was each...Ch. 2 - Determine the number of significant figures in...Ch. 2 - Determine the number of significant figures in...Ch. 2 - Determine the number of significant figures in...Ch. 2 - Determine the number of significant figures in...Ch. 2 - In which of the following pairs of numbers do both...Ch. 2 - In which of the following pairs of numbers do both...Ch. 2 - Prob. 2.35EPCh. 2 - In the pairs of numbers of Problem 2-34, tell...Ch. 2 - Prob. 2.37EPCh. 2 - Complete the following table by filling in the...Ch. 2 - Prob. 2.39EPCh. 2 - The number of people present at an outdoor rock...Ch. 2 - Round off each of the following numbers to the...Ch. 2 - Round off each of the following numbers to the...Ch. 2 - Prob. 2.43EPCh. 2 - Round off (or add zeros) to each of the following...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Without actually solving, indicate the number of...Ch. 2 - Without actually solving, indicate the number of...Ch. 2 - Prob. 2.49EPCh. 2 - Carry out the following multiplications and...Ch. 2 - Carry out the following additions and...Ch. 2 - Carry out the following additions and...Ch. 2 - What is the uncertainty in the measured value...Ch. 2 - What is the uncertainty in the measured value...Ch. 2 - For each of the following numbers, will the...Ch. 2 - For each of the following numbers, will the...Ch. 2 - Prob. 2.57EPCh. 2 - Prob. 2.58EPCh. 2 - Prob. 2.59EPCh. 2 - For each of the numbers in Problem 2-56, how many...Ch. 2 - Express the following measured values in...Ch. 2 - Express the following measured values in...Ch. 2 - Change each of the following measured values from...Ch. 2 - Change each of the following measured values from...Ch. 2 - Prob. 2.65EPCh. 2 - Prob. 2.66EPCh. 2 - What is the uncertainty, in terms of a power of...Ch. 2 - What is the uncertainty, in terms of a power of...Ch. 2 - Write each of the following numbers in scientific...Ch. 2 - Write each of the following numbers in scientific...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Prob. 2.75EPCh. 2 - Indicate whether each of the following equations...Ch. 2 - Using dimensional analysis, convert each of the...Ch. 2 - Using dimensional analysis, convert each of the...Ch. 2 - The human stomach produces approximately 2500 mL...Ch. 2 - A typical loss of water through sweating for a...Ch. 2 - The mass of premature babies is customarily...Ch. 2 - The smallest bone in the human body, which is in...Ch. 2 - What volume of water, in gallons, would be...Ch. 2 - What volume of gasoline, in milliliters, would be...Ch. 2 - An individual weighs 83.2 kg and is 1.92 m tall....Ch. 2 - An individual weighs 135 lb and is 5 ft 4 in....Ch. 2 - Prob. 2.87EPCh. 2 - Prob. 2.88EPCh. 2 - Prob. 2.89EPCh. 2 - When each of the following measurements of mass is...Ch. 2 - A sample of mercury is found to have a mass of...Ch. 2 - A sample of sand is found to have a mass of 12.0 g...Ch. 2 - Acetone, the solvent in nail polish remover, has a...Ch. 2 - Silver metal has a density of 10.40 g/cm3. What is...Ch. 2 - The density of homogenized milk is 1.03 g/mL. How...Ch. 2 - Nickel metal has a density of 8.90 g/cm3. How much...Ch. 2 - Water has a density of 1.0 g/cm3 at room...Ch. 2 - Air has a density of 1.29 g/L at room temperature....Ch. 2 - Prob. 2.99EPCh. 2 - A two-gram sample of a red-colored liquid is found...Ch. 2 - Calculate the volume, in milliliters, for each of...Ch. 2 - Calculate the volume, in milliliters, for each of...Ch. 2 - An oven for baking pizza operates at approximately...Ch. 2 - A comfortable temperature for bathtub water is...Ch. 2 - Mercury freezes at 38.9C. What is the coldest...Ch. 2 - Prob. 2.106EPCh. 2 - Prob. 2.107EPCh. 2 - Which is the higher temperature, 15C or 4F?
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