Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Question
Chapter 1, Problem 1.56E
Interpretation Introduction

(a)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a nonexponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Expert Solution
Check Mark

Answer to Problem 1.56E

The given multiplication expressed using scientific notation is shown below.

(1.44×102)(8.76×102)

The answer of the given multiplication expressed by using scientific notation is 1.26144×101.

Explanation of Solution

The given question is,

(144)(0.0876)

To express the number 144 using the scientific notation, the non-zero digits should be separated by decimal andonly one non-zero digit should be written before decimal. Thus, the number can be expressed as 1.44×102.

To express the number 0.0876 using the scientific notation, decimal moves two places to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 8.76×102.

The given multiplication expressed using scientific notation is shown below.

(1.44×102)(8.76×102)

The multiplicationscan be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of a given multiplication can be calculated as follows:

(1.44×8.76)(102+2)=12.6144×100

The above answer is adjusted to a standard position. The decimal is shifted one place to the left and the power of 10 is changed from 0 to 1. Hence, the answer of a given multiplication is 1.26144×101.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(1.44×102)(8.76×102)

The answer of the given multiplication expressed by using scientific notation is 1.26144×101.

Interpretation Introduction

(b)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplicationis to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a nonexponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Expert Solution
Check Mark

Answer to Problem 1.56E

The given multiplication expressed using scientific notation is shown below.

(7.51×102)(1.06×102)

The answer of the given multiplication expressed by using scientific notation is 7.9606×104.

Explanation of Solution

The given question is,

(751)(106)

To express the number 751 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 7.51×102.

To express the number 106 using the scientific notation, the non-zero digits should be separated by decimal andonly one non-zero digit should be written before decimal. Thus, the number can be expressed as 1.06×102.

The given multiplication expressed using scientific notation is shown below.

(7.51×102)(1.06×102)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of a given multiplication can be calculated as follows:

(7.51×1.06)(102+2)=7.9606×104

Hence, the answer of a given multiplication is 7.9606×104.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(7.51×102)(1.06×102)

The answer of the given multiplication expressed by using scientific notation is 7.9606×104.

Interpretation Introduction

(c)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a nonexponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Expert Solution
Check Mark

Answer to Problem 1.56E

The given multiplication expressed using scientific notation is shown below.

(4.22×102)(1.19×103)

The answer of the given multiplication expressed by using scientific notation is 5.0218×105.

Explanation of Solution

The given question is,

(0.0422)(0.00119)

To express the number 0.0422 using the scientific notation, decimal moves two places to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 4.22×102.

To express the number 0.00119 using the scientific notation, decimal moves three places to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 1.19×103.

The given multiplication expressed using scientific notation is shown below.

(4.22×102)(1.19×103)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of a given multiplication can be calculated as follows:

(4.22×1.19)(1023)=5.0218×105

Hence, the answer of a given multiplication is 5.0218×105.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(4.22×102)(1.19×103)

The answer of the given multiplication expressed by using scientific notation is 5.0218×105.

Interpretation Introduction

(d)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a nonexponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Expert Solution
Check Mark

Answer to Problem 1.56E

The given multiplication expressed using scientific notation is shown below.

(1.28×105)(3.16×105)

The answer of the given multiplication expressed by using scientific notation is 4.0448×100.

Explanation of Solution

The given question is,

(128,000)(0.0000316)

To express the number 128,000 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 1.28×105.

To express the number 0.0000316 using the scientific notation, decimal moves five places to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 3.16×105.

The given multiplication expressed using scientific notation is shown below.

(1.28×105)(3.16×105)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of a given multiplication can be calculated as follows:

(1.28×3.16)(1055)=4.0448×100

Hence, the answer of a given multiplication is 4.0448×100.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(1.28×105)(3.16×105)

The answer of the given multiplication expressed by using scientific notation is 4.0448×100.

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Chapter 1 Solutions

Chemistry for Today: General, Organic, and Biochemistry

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