Chapter 1, Problem 1.53P

Interpretation Introduction

(a)

Interpretation:

The answer of the given mathematical operation $53.6\times 0.41$ 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 1.53P

The answer upto two significant digits is22.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}53.6\times 0.41=2\underset{\_}{1}.976\\ \approx 22\end{array}$

Since two is the least number of significant digits that is present in 0.41, the product 21.976 must be rounded off so as to contain only two significant digits.

Therefore, the product is reported as 22.

Interpretation Introduction

(b)

Interpretation:

The difference of $25.825-3.86$ 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 1.53P

The answer upto correct significant digit is 21.96.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}25.825-3.86=21.9\underset{\_}{6}5\\ \approx 21.96\end{array}$

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 3.86, the digit 21.965 must be rounded off to contain only two decimal places.

Therefore, the difference is reported as 21.96.

Interpretation Introduction

(c)

Interpretation:

The quotient obtained on division of 65.2 by 12 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 the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.53P

The answer upto two significant digits is 5.4.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}\frac{65.2}{12}=5.\underset{\_}{4}333\\ \approx 5.4\end{array}$

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

Since two is the least number of significant digitsthat is present in 12, the product 5.4333 must be rounded off to contain only two significant digits.

Therefore, the quotient is reported as 5.4 correct upto two significant figures.

Interpretation Introduction

(d)

Interpretation:

The sum of $41.0+9.135$ 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 result is reported to least number of significant digits. This means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.53P

The answer upto three significant digits is50.1.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}41.0+9.135=50.\underset{\_}{1}35\\ \approx 50.1\end{array}$

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

Since one is the least number of decimal places that is present in 41.0, the digit 3 must be rounded off to contain only one decimal place.

Therefore, the sum is reported as 50.1.

Interpretation Introduction

(e)

Interpretation:

The answer of the given mathematical operation $694.2\times 0.2$ 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 result is reported to least number of significant digits. This means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.53P

The answer is reported as $1.4\times {10}^2$.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}694.2\times 0.2=\underset{\_}{1}38.84\\ \approx 1.4\times {10}^2\end{array}$

Since one is the least number of significant digits that is present in 0.2and hence the product 130.84 must be rounded off so as to contain only one significant digit.

Therefore, the product is reported as $1.4\times {10}^2$.

Interpretation Introduction

(f)

Interpretation:

The difference of $1045-1.26$ 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 result is reported to least number of significant digits. This means the digits that follow the least number of significant digits are rounded off in the result.

Answer to Problem 1.53P

The answer upto two significant digits is1044.

Explanation of Solution

The mathematical operation is carried out as follows:

  $\begin{array}{c}1045-1.26=104\underset{\_}{3}.74\\ \approx \text{1044}\end{array}$

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

Since zero is the least number of decimal places that is present in 1045,the final result should contain zero decimal places.

Therefore, the difference is reported as 1044.