Chapter 1, Problem 1.54P

Interpretation Introduction

(a)

Interpretation:

The answer of the given mathematical operation $49682\times 0.80$ is to be reported to appropriate number of significant figures.

Concept introduction:

During measurement of the physical quantity, there always occurs a digit that is not known with certainty. The significant digits carry significance for the measurement of that physical quantity.

There are certain thumb rules for identification of number of significant digits in a number.

1. All the trailing zeroes after the decimal point are not significant.

2. Zero that is placed to fix a decimal position is not significant.

3. Zero is only significant when it lies between two natural numbers.

For example, 0.00456 has three significant digits.

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed, operation is carried out and the result is reported to least number of significant digits. This means that the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.54P

The answer upto correct significant digits is40000.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}49682\times 0.80=3\underset{\_}{9}745.6\\ \approx 40000\end{array}$

Since two is the least number of significant digits that is present in 0.80, the product 39745.6 must be rounded off to contain only two significant digits.

Therefore, the product is reported as 40000.

Interpretation Introduction

(b)

Interpretation:

The sum of $66.815+2.82$ is to be reported to appropriate number of significant figures.

Concept introduction:

During measurement of the physical quantity, there always occurs a digit that is not known with certainty. The significant digits carry significance for the measurement of that physical quantity.

There are certain thumb rules for identification of number of significant digits in a number.

1. All the trailing zeroes after the decimal point are not significant.

2. Zero that is placed to fix a decimal position is not significant.

3. Zero is only significant when it lies between two natural numbers.

For example, 0.00456 has three significant digits.

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed, operation is carried out and the result is reported to least number of significant digits. This means that the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.54P

The answer upto correct number of decimal places is 69.64.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}66.815+2.82=69.6\underset{\_}{3}5\\ \approx \text{69}\text{.64}\end{array}$

Since in addition or subtraction the result is reported that has least number of decimal places all the other digits are rounded off.

Since two is the least number of decimal places that is present in 2.82, the digit 5 in difference 63.635must be rounded off to contain only two decimal places.

Therefore, the sum is reported as 69.64.

Interpretation Introduction

(c)

Interpretation:

The quotient obtained on division of 1000 by 2.34 is to be reported to appropriate number of significant figures.

Concept introduction:

During measurement of the physical quantity, there always occurs a digit that is not known with certainty. The significant digits are digits that carry significance for the measurement of that physical quantity.

There are certain thumb rules for identification of number of significant digits in a number.

1. All the trailing zeroes after the decimal point are not significant.

2. Zero that is placed to fix a decimal position is not significant.

3. Zero is only significant when it lies between two natural numbers.

For example, 0.00456 has three significant digits.

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed operation is carried out and the final result is reported to least number of significant digits which means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.54P

The quotient obtained on division of 1000 by 2.34 is 300.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}\frac{1000}{2.34}=\underset{\_}{4}27.35042\\ \approx 400\end{array}$

Since in division the result is reported that has least number of significant figures all the other digits are rounded off.

Since one is the least number of significant figures that is present in 1000 and therefore 427.35042 must be rounded off to obtain one significant figure.

Therefore the quotient is reported as 400.

Interpretation Introduction

(d)

Interpretation:

The difference of numbers $21-0.88$ is to be reported to appropriate number of significant figures.

Concept introduction:

During measurement of the physical quantity there always occurs a digit that is not known with certainty. The significant digits are digits that carry significance for the measurement of that physical quantity.

There are certain thumb rules for identification of number of significant digits in a number.

1. All the trailing zeroes after the decimal point are not significant.

2. Zero that is placed to fix a decimal position is not significant.

3. Zero is only significant when it lies between two natural numbers.

For example, 0.00456 has three significant digits.

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed operation is carried out and the final result is reported to least number of significant digits which means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.54P

The difference of numbers $21-0.88$ is 20.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}21-0.88=2\underset{\_}{0}.12\\ \approx 20\end{array}$

Since in addition or subtraction the result is reported that has least number of decimal places and all the other digits are rounded off.

Here the least number of decimal places is zero so answer is reported that has zero decimal places.

Therefore the difference is reported as 20.

Interpretation Introduction

(e)

Interpretation:

The quotient obtained on division of 25000 by 0.4356 is to be reported to appropriate number of significant figures.

Concept introduction:

During measurement of the physical quantity there always occurs a digit that is not known with certainty. The significant digits are digits that carry significance for the measurement of that physical quantity.

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed operation is carried out and the final result is reported to least number of significant digits which means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.54P

The answer is reported as 57000.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}\frac{25000}{0.4356}=\text{5}\underset{\_}{\text{7}}\text{392}\text{.1028}\\ \approx 57000\end{array}$

Since two is the least number of significant digits that is present in 25000 hence the quotient 57392.1028 must be rounded off so as to contain only two significant digits.

Therefore the answer is reported as 57000.

Interpretation Introduction

(f)

Interpretation:

The sum of the given numbers $21.5381+26.55$ is to be reported to appropriate number of significant figures.

Concept introduction:

Rules for addition of significant figures are as follows:

While the addition or subtraction operation is being performed, operation is carried out and the final result is reported to least number of decimal places. Digits present at all the other places are rounded off.

While the multiplication or division operation is being performed operation is carried out and the final result is reported to least number of significant digits which means the digits that follow the least number of significant digits are rounded off in the result

Answer to Problem 1.54P

The sum of the numbers $21.5381+26.55$ is 48.09.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}21.5381+26.55=48.0\underset{\_}{8}81\\ \approx 48.09\end{array}$

Since two is the least number of decimal places that is present in 26.55 hence the final result should contain two decimal places. Therefore the digits that follow 8 must be dropped off. And since the digit to be dropped is greater than 8 therefore previous digit must be increased by one unit.

Therefore the sum is reported as 48.09.