Chapter 1, Problem 1.55E

Interpretation Introduction

(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 $M\times {10}^n$. 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.

Answer to Problem 1.55E

The answer of the given multiplication expressed by using scientific notation is $2.646\times {10}^{-2}$.

Explanation of Solution

The given question is,

$\left(6.3\times {10}^5\right)\left(4.2\times {10}^{-8}\right)$

The multiplication can be expressed as follows:

$\left(a\times {10}^y\right)\left(b\times {10}^z\right)=\left(a\times b\right)\left({10}^{y+z}\right)$

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

$\begin{array}{r}\left(6.3\times 4.2\right)\left({10}^{-8+5}\right)\\ & =& 26.46\times {10}^{-3}\end{array}$

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 $2.646\times {10}^{-2}$.

Conclusion

The answers of the given multiplication expressed by using scientific notation is $2.646\times {10}^{-2}$.

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 $M\times {10}^n$. 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.

Answer to Problem 1.55E

The answer of the given multiplication expressed by using scientific notation is $3.92\times {10}^{-7}$.

Explanation of Solution

The given question is,

$\left(2.8\times {10}^{-3}\right)\left(1.4\times {10}^{-4}\right)$

The multiplication can be expressed as follows:

$\left(a\times {10}^y\right)\left(b\times {10}^z\right)=\left(a\times b\right)\left({10}^{y+z}\right)$

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

$\begin{array}{r}\left(2.8\times 1.4\right)\left({10}^{-3-4}\right)\\ & =& 3.92\times {10}^{-7}\end{array}$

Hence, the answer of a given multiplication is $3.92\times {10}^{-7}$.

Conclusion

The answer of the given multiplication expressed by using scientific notation is $3.92\times {10}^{-7}$.

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 $M\times {10}^n$. 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.

Answer to Problem 1.55E

The answer of the given multiplication expressed by using scientific notation is $5.504\times {10}^0$.

Explanation of Solution

The given question is,

$\left(8.6\times {10}^2\right)\left(6.4\times {10}^{-3}\right)$

The multiplications can be expressed as follows:

$\left(a\times {10}^y\right)\left(b\times {10}^z\right)=\left(a\times b\right)\left({10}^{y+z}\right)$

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

$\begin{array}{r}\left(8.6\times 6.4\right)\left({10}^{2-3}\right)\\ & =& 55.04\times {10}^{-1}\end{array}$

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 $5.504\times {10}^0$.

Conclusion

The answer of the given multiplication expressed by using scientific notation is $5.504\times {10}^0$.

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 $M\times {10}^n$. 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.

Answer to Problem 1.55E

The answer of the given multiplication expressed by using scientific notation is $1.274\times {10}^8$.

Explanation of Solution

The given question is,

$\left(9.1\times {10}^4\right)\left(1.4\times {10}^3\right)$

The multiplications can be expressed as follows:

$\left(a\times {10}^y\right)\left(b\times {10}^z\right)=\left(a\times b\right)\left({10}^{y+z}\right)$

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

$\begin{array}{r}\left(9.1\times 1.4\right)\left({10}^{4+3}\right)\\ & =& 12.74\times {10}^7\end{array}$

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 $1.274\times {10}^8$.

Conclusion

The answer of the given multiplication expressed by using scientific notation is $1.274\times {10}^8$.

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 $M\times {10}^n$. 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.

Answer to Problem 1.55E

The answer of the given multiplication expressed by using scientific notation is $2.257\times {10}^3$.

Explanation of Solution

The given question is,

$\left(3.7\times {10}^5\right)\left(6.1\times {10}^{-3}\right)$

The multiplications can be expressed as follows:

$\left(a\times {10}^y\right)\left(b\times {10}^z\right)=\left(a\times b\right)\left({10}^{y+z}\right)$

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

$\begin{array}{r}\left(3.7\times 6.1\right)\left({10}^{5-3}\right)\\ & =& 22.57\times {10}^2\end{array}$

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 $2.257\times {10}^3$.

Conclusion

The answer of the given multiplication expressed by using scientific notation is $2.257\times {10}^3$.