Chemistry for Today: General  Organic  and Biochemistry
Chemistry for Today: General Organic and Biochemistry
9th Edition
ISBN: 9781337514576
Author: Seager
Publisher: Cengage
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Textbook Question
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Chapter 1, Problem 1.74E

Do the following calculations and use the correct number of significant figures in your answers. Assume all numbers are the results of measurements. In calculations involving both addition/subtraction and multiplication/division, it is usually better to do additions/subtractions first.

a. ( 0.0267   +   0.0019 ) ( 4.626 ) 28.7794

b. 212.6     21.88 86.37

c. 27.99   18.07   4.63     0.88

d. 18.87 2.46     18.07 0.88

(HINT: Do divisions first, then subtract.)

e. ( 8.46     2.09 ) ( 0.51   +   0.22 ) ( 3.74   +   0.07 ) ( 0.16   +   0.2 )

f. 12.06     11.84 0.271

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 0.00460 and three significant figures are present.

Explanation of Solution

The given problem is,

(0.0267+0.0019)(4.626)28.7794

The calculation is as follows:

(0.0267+0.0019)(4.626)28.7794=0.0286(4.626)28.7794=0.132303628.7794=0.0045971632487126

The lowest number of significant figures in the problem is three. Therefore, the answer is expressed by using three significant figures. The non-significant figure which is dropped is 7 and it is greater than five. Thus, one unit is added to last digit remained. Hence, the result of a given problem is 0.00460.

Conclusion

The result of the given calculation is 0.00460 and three significant figures are present.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 2.208 and four significant figures are present.

Explanation of Solution

The given problem is,

212.621.8886.37

The calculation is as follows:

212.621.8886.37=190.7286.37=2.208174134537455

The lowest number of significant figures in the problem is four. Therefore, the answer is expressed by using four significant figures. The non-significant figure which is dropped is 1 and it is lesser than five. Thus, one unit is not added to last digit. Hence, the result of a given problem is 2.208.

Conclusion

The result of the given calculation is 2.208 and four significant figures are present.

Expert Solution
Check Mark
Interpretation Introduction

(c)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 2.65 and three significant figures are present.

Explanation of Solution

The given problem is,

27.9918.074.630.88

The calculation is as follows:

27.9918.074.630.88=9.923.75=2.6453333

The lowest number of significant figures in the problem is three. Therefore, the answer is expressed by using three significant figures. The non-significant figure which is dropped is 5. Thus, one unit is added to last digit. Hence, the result of a given problem is 2.65.

Conclusion

The result of the given calculation is 2.65 and three significant figures are present.

Expert Solution
Check Mark
Interpretation Introduction

(d)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 12.86 and two significant figures are present.

Explanation of Solution

The given problem is,

18.872.4618.070.88

The calculation is as follows:

18.872.4618.070.88=7.6720.53=12.86

The answer is rounded off to that number which contains smallest number of places after the decimal. Hence, the result of a given problem is 12.86.

Conclusion

The result of the given calculation is 12.86 and 13.0 with two significant figures are present.

Expert Solution
Check Mark
Interpretation Introduction

(e)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 3.3903 and five significant figures are present.

Explanation of Solution

The given problem is,

(8.462.09)(0.51+0.22)(3.74+0.07)(0.16+0.2)

The calculation is as follows:

(8.462.09)(0.51+0.22)(3.74+0.07)(0.16+0.2)=6.37×0.733.81×0.36=4.65011.3716=3.390274132400117

The lowest number of significant figures in the problem is five. Therefore, the answer is expressed by using five significant figures. The non-significant figure which is dropped is 7, it is greater than five. Thus, one unit is added to last digit remained. Hence, the result of a given problem is 3.3903.

Conclusion

The result of the given calculation is 3.3903 and five significant figures are present.

Expert Solution
Check Mark
Interpretation Introduction

(f)

Interpretation:

The calculations are to be expressed by using correct number of significant figures.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and 10 raised to some power. Significant figures are used to express a measurement in scientific notation. The significant figures reflect the closeness of measured values to the standard values.

Answer to Problem 1.74E

The result of the given calculation is 0.81 and two significant figures are present.

Explanation of Solution

The given problem is,

12.0611.840.271

The calculation is as follows:

12.0611.840.271=0.220.271=0.8118081180811808

The lowest number of significant figures in the problem is two. Therefore, the answer is expressed by using two significant figures. The non-significant figure which is dropped is 1, it is lesser than five. Thus, one unit is not added to last digit remained. Hence, the result of a given problem is 0.81.

Conclusion

The result of the given calculation is 0.81 and two significant figures are present.

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Chapter 1 Solutions

Chemistry for Today: General Organic and Biochemistry

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