(a) Interpretation: 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 non-exponential term and exponential term in the form of M × 10 n . 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.
(a) Interpretation: 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 non-exponential term and exponential term in the form of M × 10 n . 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.
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 non-exponential 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
Answer to Problem 1.55E
The answer of the given multiplication expressed by using scientific notation is 2.646×10−2.
Explanation of Solution
The given question is,
(6.3×105)(4.2×10−8)
The multiplication can be expressed as follows:
(a×10y)(b×10z)=(a×b)(10y+z)
The answer of the given multiplication can be calculated as follows:
(6.3×4.2)(10−8+5)=26.46×10−3
The above answer is adjusted to a standard position. The decimal is shifted towards one place to the left and the power of 10 is changed from −3 to −2. Hence, the answer of a given multiplication is 2.646×10−2.
Conclusion
The answers of the given multiplication expressed by using scientific notation is 2.646×10−2.
Interpretation Introduction
(b)
Interpretation:
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 non-exponential 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
Answer to Problem 1.55E
The answer of the given multiplication expressed by using scientific notation is 3.92×10−7.
Explanation of Solution
The given question is,
(2.8×10−3)(1.4×10−4)
The multiplication can be expressed as follows:
(a×10y)(b×10z)=(a×b)(10y+z)
The answer of a given multiplication can be calculated as follows:
(2.8×1.4)(10−3−4)=3.92×10−7
Hence, the answer of a given multiplication is 3.92×10−7.
Conclusion
The answer of the given multiplication expressed by using scientific notation is 3.92×10−7.
Interpretation Introduction
(c)
Interpretation:
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 non-exponential 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
Answer to Problem 1.55E
The answer of the given multiplication expressed by using scientific notation is 5.504×100.
Explanation of Solution
The given question is,
(8.6×102)(6.4×10−3)
The multiplications can be expressed as follows:
(a×10y)(b×10z)=(a×b)(10y+z)
The answer of a given fraction can be calculated as follows:
(8.6×6.4)(102−3)=55.04×10−1
The above answer is adjusted to a standard position. The decimal is shifted towards one place to the left and the power of 10 is changed from −1 to 0. Hence, the answer of a given multiplication is 5.504×100.
Conclusion
The answer of the given multiplication expressed by using scientific notation is 5.504×100.
Interpretation Introduction
(d)
Interpretation:
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 non-exponential 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
Answer to Problem 1.55E
The answer of the given multiplication expressed by using scientific notation is 1.274×108.
Explanation of Solution
The given question is,
(9.1×104)(1.4×103)
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:
(9.1×1.4)(104+3)=12.74×107
The above answer is adjusted to a standard position. The decimal is shifted towards one place to the left and the power of 10 is changed from 7 to 8. Hence, the answer of the given multiplication is 1.274×108.
Conclusion
The answer of the given multiplication expressed by using scientific notation is 1.274×108.
Interpretation Introduction
(e)
Interpretation:
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 non-exponential 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
Answer to Problem 1.55E
The answer of the given multiplication expressed by using scientific notation is 2.257×103.
Explanation of Solution
The given question is,
(3.7×105)(6.1×10−3)
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:
(3.7×6.1)(105−3)=22.57×102
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 2 to 3. Hence, the answer of a given multiplication is 2.257×103.
Conclusion
The answer of the given multiplication expressed by using scientific notation is 2.257×103.
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