Chapter 1, Problem 1.54P

(a)

Interpretation Introduction

Interpretation:

Each number is to be rounded off to two significant figures.

Concept introduction:

Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit. The number of a certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.

To determine the number of significant figures in a quantity following steps are followed.

1. The quantity must have a decimal point.

2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.

3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.

4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, the exponential notation can be used to avoid confusion. For example, in 4300 has 3 significant figures. It can be expressed in scientific notation as $4.30\times {10}^3$ or

$4.300\times {10}^3$. The number of significant figures in $4.30\times {10}^3$ and $4.300\times {10}^3$ is 3 and 4 respectively.

5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.

(b)

Interpretation Introduction

Interpretation:

Each number is to be rounded off to four significant figures.

Concept introduction:

Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit. The number of a certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.

To determine the number of significant figures in a quantity following steps are followed.

1. The quantity must have a decimal point.

2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.

3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.

4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, the exponential notation can be used to avoid confusion. For example, in 4300 has 3 significant figures. It can be expressed in scientific notation as $4.30\times {10}^3$ or

$4.300\times {10}^3$. The number of significant figures in $4.30\times {10}^3$ and $4.300\times {10}^3$ is 3 and 4 respectively.

5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.

(c)

Interpretation Introduction

Interpretation:

Each number is to be rounded off to three significant figures.

Concept introduction:

Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit. The number of a certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.

To determine the number of significant figures in a quantity following steps are followed.

1. The quantity must have a decimal point.

2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.

3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.

4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, the exponential notation can be used to avoid confusion. For example, 4300 has 3 significant figures. It can be expressed in scientific notation as $4.30\times {10}^3$ or 

$4.300\times {10}^3$. The number of significant figures in $4.30\times {10}^3$ and $4.300\times {10}^3$ is 3 and 4 respectively.

5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.