Chapter 5, Problem 26A

(a)

Interpretation Introduction

Interpretation: The given number $0.00003562$ needs to be written in two significant digits and in scientific notation.

Concept Introduction: Rules used for rounding off numbers are as follows:

If the digit to be removed:

1. Is less than 5, then digit before it remains the same.
2. Is greater than 5, then digit before it is increased by 1 unit.
3. Is equal to five, then if the digit before it is odd then it is increased by 1 unit and if the digit is even then it remains the same.

Answer to Problem 26A

  $0.00003562$ is rounded off to $3.6\times {10}^{-5}$ .

Explanation of Solution

At first, the number is written as follows:

  $0.00003562=3.56\times {10}^{-5}$

The number is rounded off to two significant figures, so, look at the digit which is to be removed. The digit to be removed is 6 that is greater than 5. Hence, the digit before it is increased by 1. Therefore, $0.00003562$ is rounded off to $3.6\times {10}^{-5}$ .

(b)

Interpretation Introduction

Interpretation: The given number $986,622$ needs to be written in two significant digits and in scientific notation.

Concept Introduction: Rules used for rounding off numbers are as follows:

If the digit to be removed:

1. Is less than 5, then digit before it remains the same.
2. Is greater than 5, then digit before it is increased by 1 unit.
3. Is equal to five, then if the digit before it is odd then it is increased by 1 unit and if the digit is even then it remains the same.

Answer to Problem 26A

  $986,622$ is rounded off to $9.9\times {10}^4$ .

Explanation of Solution

To round off the given number to two significant figures, first look for the digit which is to be removed. In this case, the digit to be removed is larger than 5. Thus, the number becomes $986,000$ . Therefore, $986,622$ is rounded off to $9.9\times {10}^4$ in the scientific notation.

(c)

Interpretation Introduction

Interpretation: The given number $36.3\times {10}^5$ needs to be rounded off to two significant digits.

Concept Introduction: Rules used for rounding off numbers are as follows:

If the digit to be removed:

1. Is less than 5, then digit before it remains the same.
2. Is greater than 5, then digit before it is increased by 1 unit.
3. Is equal to five, then if the digit before it is odd then it is increased by 1 unit and if the digit is even then it remains the same.

Answer to Problem 26A

  $36.3\times {10}^5$ is rounded off to $3.6\times {10}^6$ .

Explanation of Solution

The number $36.3\times {10}^5$ needs to be rounded off to two significant digits.

Firstly, look for the digit which is to be removed. The digit to be removed is smaller than 5. Hence, no change takes place in the digit before it. Therefore, $36.3\times {10}^5$ is rounded off to $3.6\times {10}^6$ .

(d)

Interpretation Introduction

Interpretation: The given number $0.8515\times {10}^4$ needs to be rounded off to two significant digits.

Concept Introduction: Rules used for rounding off numbers are as follows:

If the digit to be removed:

1. Is less than 5, then digit before it remains the same.
2. Is greater than 5, then digit before it is increased by 1 unit.
3. Is equal to five, then if the digit before it is odd then it is increased by 1 unit and if the digit is even then it remains the same.

Answer to Problem 26A

  $0.8515\times {10}^4$ is rounded off to $8.5\times {10}^3$ .

Explanation of Solution

First, look at the digit which is to be removed. In this case, the digit to be removed is smaller than 5. Hence, no change in the digit before it takes place. Therefore, $0.8515\times {10}^4$ is rounded off to $8.5\times {10}^3$ .