Chapter 2, Problem 2.57EP

(a)

Interpretation Introduction

Interpretation:

0.0123 when expressed in scientific notation, the number of places the decimal point has to be moved must be given.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “${\text{A x 10}}^{\text{n}}$, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

(b)

Interpretation Introduction

Interpretation:

375,000 when expressed in scientific notation, the number of places the decimal point has to be moved must be given.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “${\text{A x 10}}^{\text{n}}$, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

(c)

Interpretation Introduction

Interpretation:

0.100 when expressed in scientific notation, the number of places the decimal point has to be moved must be given.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “${\text{A x 10}}^{\text{n}}$, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.

(d)

Interpretation Introduction

Interpretation:

68.75 when expressed in scientific notation, the number of places the decimal point has to be moved must be given.

Concept Introduction:

In scientific work, large and very small numbers occurs frequently.  But it is been observed that, to record these vast numbers or very small numbers is difficult because, the numbers may get missed while recording them.  It is time consuming and the possibilities of error occurrence are also high.  Hence to overcome these demerits, a method called scientific notation is used.  Scientific notation is a numerical system where a decimal number is expressed as product of two number between 1 and 10 (coefficient) and 10 that is raised to power (exponential term).  In this method the numbers are expressed in form of “${\text{A x 10}}^{\text{n}}$, where A is called the co-efficient, n is the whole number and 10 is called the exponential term.  This way of expressing is much easier and error free.  If the decimal number is 10 or greater than 10, then the exponent is positive and if the decimal number is less than 1, then the exponent is negative.