Chapter 3, Problem 10E

Interpretation Introduction

(a)

Interpretation:

The following operation $9.25\times {10}^{-7}+8.60\times {10}^{-4}$ is to be completed.

Concept introduction:

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, the binary operation deals with two kinds of values includes addition, subtraction, multiplication and division.

Answer to Problem 10E

The solution for the following operation $9.25\times {10}^{-7}+8.60\times {10}^{-4}=8.61\times {10}^{-4}$

Explanation of Solution

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, binary operation deals with two kinds of values includes addition, subtraction, multiplication and division.

Different types of operations are;

Division: in this method the variables divided which is raised to a power is equal to subtracting their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ divided by ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a-b}}$

Multiplications: in the method the variables multiplied which is raised to a power is equal to adding their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ times ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a+b}}$ Based on the operation methods, the given operation can be solved as follows;

$\begin{array}{l}9.25\times {10}^{-7}+8.60\times {10}^{-4}=?\\ \text{on}\text{rearranging}\text{the}\text{values, we}\text{get}\\ =-\left(0.00925+8.60\right)\left({10}^{-4}\right)\\ =\left(8.61\times {10}^{-4}\right)\\ \text{Since}\text{by}\text{formula,}\text{Since, by}\text{formula }\frac{{\text{a}}^m}{a^n}=a^{m-n}=\left(8.61\times {10}^{-4}\right)\end{array}$

Conclusion

The solution for the following operation $9.25\times {10}^{-7}+8.60\times {10}^{-4}=8.61\times {10}^{-4}$

Interpretation Introduction

(b)

Interpretation:

The following operation $\frac{7.54\times {10}^{-5}}{\left(9.25\times {10}^{-7}\right)\left(8.60\times {10}^{-4}\right)}\text{is}9.4\times {10}^4$ is to be completed.

Concept introduction:

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, binary operation deals with two kind of values includes addition, subtraction, multiplication and division.

Answer to Problem 10E

The solution for the following operation $\frac{8.60\times {10}^{-4}+4.23\times {10}^5}{1.72\times {10}^{-4}}\text{is}2.5\times {10}^9$.

Explanation of Solution

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, binary operation deals with two kind of values includes addition, subtraction, multiplication and division.

Different types of operations are;

Division: in this method the variables divided which is raised to a power is equal to subtracting their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ divided by ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a-b}}$

Multiplications: in the method the variables multiplied which is raised to a power is equal to adding their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ times ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a+b}}$

Based on the operation methods, the given operation can be solved as follows;

$\begin{array}{l}\frac{8.60\times {10}^{-4}+4.23\times {10}^5}{1.72\times {10}^{-4}}=?\\ \text{on}\text{rearranging}\text{the}\text{values, we}\text{get}\\ =\frac{0.000860\times 423000}{\left({4.023}^5\right)}\\ \text{Since}\text{by}\text{formula,}\text{Since, by}\text{formula }\frac{{\text{a}}^m}{a^n}=a^{m-n}\\ =2.5\times {10}^9\end{array}$

Conclusion

The solution for the following operation $\frac{8.60\times {10}^{-4}+4.23\times {10}^5}{1.72\times {10}^{-4}}\text{is}2.5\times {10}^9$.

Interpretation Introduction

(c)

Interpretation:

The following operation $\frac{7.54\times {10}^{-5}}{\left(9.25\times {10}^{-7}\right)\left(8.60\times {10}^{-4}\right)}$ is to be completed.

Concept introduction:

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, binary operation deals with two kind of values includes addition, subtraction, multiplication and division.

Answer to Problem 10E

The solution for the following operation $\frac{7.54\times {10}^{-5}}{\left(9.25\times {10}^{-7}\right)\left(8.60\times {10}^{-4}\right)}\text{is}9.4\times {10}^4$.

Explanation of Solution

An operation is defined as calculation of an output value from zero or more input values. Principally, binary and unary operations are most commonly analyzed operations.

Moreover, unary operations involve only one value such as trigonometric functions and negations. Whereas, binary operation deals with two kind of values includes addition, subtraction, multiplication and division.

Different types of operations are;

Division: in this method the variables divided which is raised to a power is equal to subtracting their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ divided by ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a-b}}$

Multiplications: in the method the variables multiplied which is raised to a power is equal to adding their exponents raised to a power.

${\text{Ex:x}}^{\text{a}}$ times ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a+b}}$

Based on the operation methods, the given operation can be solved as follows;

$\begin{array}{l}\frac{7.54\times {10}^{-5}}{\left(9.25\times {10}^{-7}\right)\left(8.60\times {10}^{-4}\right)}=?\\ \text{on}\text{rearranging}\text{the}\text{values, we}\text{get,}\\ \text{=}\frac{7.54\times {10}^{-5}}{(9.25\times 8.60)\left({10}^{-7}{10}^{-4}\right)}\\ =\frac{\left(7.54\times {10}^{-5}\right)}{\left(79.55\times {10}^{-11}\right)}\\ \text{Since, by}\text{formula }\frac{{\text{a}}^m}{a^n}=a^{m-n}\\ =9.4\times {10}^4\end{array}$

Conclusion

The solution for the following operation $\frac{7.54\times {10}^{-5}}{\left(9.25\times {10}^{-7}\right)\left(8.60\times {10}^{-4}\right)}\text{is}9.4\times {10}^4$.^s