Chapter 2, Problem 2.59EP

(a)

Interpretation Introduction

Interpretation:

The number of significant figure that has to be present when 0.0123 is expressed in scientific notation has to 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.

Significant figures are the digits that are present in a measurement which is known with certainty plus one digit that is estimated.  Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  It depends on where the zero appears.  Leading zeros in the front of any number are never significant.  Zeros between the numbers are significant.  Zeros appearing at the last (trailing zeros) are significant if a decimal point is there in the number.  The last digit that produces uncertainty is called the estimated digit.

(b)

Interpretation Introduction

Interpretation:

The number of significant figure that has to be present when 375,000 is expressed in scientific notation has to 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.

Significant figures are the digits that are present in a measurement which is known with certainty plus one digit that is estimated.  Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  It depends on where the zero appears.  Leading zeros in the front of any number are never significant.  Zeros between the numbers are significant.  Zeros appearing at the last (trailing zeros) are significant if a decimal point is there in the number.  The last digit that produces uncertainty is called the estimated digit.

(c)

Interpretation Introduction

Interpretation:

The number of significant figure that has to be present when 0.100 is expressed in scientific notation has to 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.

Significant figures are the digits that are present in a measurement which is known with certainty plus one digit that is estimated.  Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  It depends on where the zero appears.  Leading zeros in the front of any number are never significant.  Zeros between the numbers are significant.  Zeros appearing at the last (trailing zeros) are significant if a decimal point is there in the number.  The last digit that produces uncertainty is called the estimated digit.

(d)

Interpretation Introduction

Interpretation:

The number of significant figure that has to be present when 68.75 is expressed in scientific notation has to 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.

Significant figures are the digits that are present in a measurement which is known with certainty plus one digit that is estimated.  Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  It depends on where the zero appears.  Leading zeros in the front of any number are never significant.  Zeros between the numbers are significant.  Zeros appearing at the last (trailing zeros) are significant if a decimal point is there in the number.  The last digit that produces uncertainty is called the estimated digit.