Chapter 3, Problem 9E

Interpretation Introduction

(a)

Interpretation:

The following operation $\frac{\left(9.84\times {10}^3\right)}{\left(6.12\times {10}^3\right)\left(4.27\times {10}^7\right)}\text{is}\text{3}\text{.77}\times {\text{10}}^{-8}$ is to be completed.

Concept introduction:

An operation is a calculation from zero or more values (operands) of input to a value of output. The most widely analyzed operations are binary and unary operations. Moreover, binary operations deal with two values and it includes addition, subtraction, multiplication, and division operations deals with the one value and trigonometric functions.

Answer to Problem 9E

The solution for the following operation $\frac{\left(9.84\times {10}^3\right)}{\left(6.12\times {10}^3\right)\left(4.27\times {10}^7\right)}\text{is}\text{3}\text{.77}\times {\text{10}}^{-8}$

Explanation of Solution

Principally, operation can be defined as a calculation from zero or more values (operands) of input to a value of output. The most widely analyzed operations are binary and unary operations. The binary operations deal with two values and it includes addition, subtraction, multiplication, and division operations deals with the one value and trigonometric functions.

Different types of operations are;

Multiplications: It deals with multiplying the variables raised to a power involves adding their exponents. ${\text{Ex:x}}^{\text{a}}$ times ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a+b}}$

Division: It deals with dividing the variables raised to a power involves subtracting their exponents. ${\text{Ex:x}}^{\text{a}}$ divided by ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a-b}}$

Exponentiation: It deals with exponentiation of variables raised to a power involves multiplying the exponents. ${\text{Ex:x}}^{\text{a}}$ raised to the b power = ${\text{x}}^{\text{a b}}$

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

$\begin{array}{l}\frac{\left(9.84\times {10}^3\right)}{\left(6.12\times {10}^3\right)\left(4.27\times {10}^7\right)}=?\\ \text{on}\text{rearranging}\text{the}\text{values, we}\text{get,}\\ \text{=}\frac{\left(9.84\times {10}^3\right)}{\left(6.12\right)\left(4.27\right)\left({10}^3{10}^7\right)}\\ =\frac{\left(9.84\times {10}^3\right)}{\left(26.13\times {10}^{10}\right)}\\ =\frac{\left(9.84\times {10}^3\right)}{\left(2.61\times {10}^{11}\right)}\\ \text{Since, by}\text{formula }\frac{{\text{a}}^m}{a^n}=a^{m-n}\\ =3.77\times {10}^{-8}\end{array}$

Conclusion

The following operation $\frac{\left(9.84\times {10}^3\right)}{\left(6.12\times {10}^3\right)\left(4.27\times {10}^7\right)}\text{is}\text{3}\text{.77}\times {\text{10}}^{-8}$ is calculated.

Interpretation Introduction

(b)

Interpretation:

The following operation $\frac{\left(4.36\times {10}^8\right)\left(1.82\times {10}^3\right)}{0.0856\left(4.7\times {10}^6\right)}\text{is}2.0\times {10}^6$ is to be completed.

Concept introduction:

An operation is a calculation from zero or more values (operands) of input to a value of output. The most widely analyzed operations are binary and unary operations. Moreover, binary operations deal with two values and it includes addition, subtraction, multiplication, and division operations deals with the one value and trigonometric functions.

Answer to Problem 9E

The solution for the following operation $\frac{\left(4.36\times {10}^8\right)\left(1.82\times {10}^3\right)}{0.0856\left(4.7\times {10}^6\right)}\text{is}2.0\times {10}^6$

Explanation of Solution

Principally, operation can be defined as a calculation from zero or more values (operands) of input to a value of output. The most widely analyzed operations are binary and unary operations. The binary operations deal with two values and it includes addition, subtraction, multiplication, and division operations deals with the one value and trigonometric functions.

Different types of operations are;

Multiplications: It deals with multiplying the variables raised to a power involves adding their exponents. ${\text{Ex:x}}^{\text{a}}$ times ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a+b}}$

Division: It deals with dividing the variables raised to a power involves subtracting their exponents ${\text{Ex:x}}^{\text{a}}$ divided by ${\text{x}}^{\text{b}}{\text{= x}}^{\text{a-b}}$

Exponentiation: It deals with exponentiation of variables raised to a power involves multiplying the exponents. ${\text{Ex:x}}^{\text{a}}$ raised to the b power = ${\text{x}}^{\text{a b}}$

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

$\begin{array}{l}\frac{\left(4.36\times {10}^8\right)(1.82\times {10}^3)}{0.0856\left(4.7\times {10}^6\right)}=?\\ \text{on}\text{rearranging}\text{the}\text{values, we}\text{get,}\\ \text{=}\frac{\left(4.36\right)\left(1.82\right)\left({10}^8{10}^3\right)}{\left(8.56\right)\left(4.7\right)\left({10}^{-2}{10}^6\right)}\\ =\frac{\left(7.93\times {10}^{11}\right)}{\left(4.023\times {10}^5\right)}\\ \text{Since, by}\text{formula }\frac{{\text{a}}^m}{a^n}=a^{m-n}\\ =2.0\times {10}^6\end{array}$

Conclusion

The solution for the following operation $\frac{\left(4.36\times {10}^8\right)\left(1.82\times {10}^3\right)}{0.0856\left(4.7\times {10}^6\right)}\text{is}2.0\times {10}^6$