Chapter 1, Problem 1.84SP

Interpretation Introduction

(a)

Interpretation:

Whether the statement “ $1\text{ft}$ is equal to $12\text{in}$ ” uses an exact number or not should be stated.

Concept introduction:

An exact number is a completely certain number, that is, which can be counted. For example, 1 kilometer has exactly 1000 meter or 1 dozen has 12 number of items, which is also an exact number.

Exact numbers have infinite significant figures and zero error or uncertainty. Example 12 has infinite significant figures but 12.00 has 4 significant figures. To exactly determine the uncertainty in the final answer of measurement, significant figures are calculated.

The rules for counting significant figures will be as follows:

• Numbers that are non-zero are significant figures.
• The zeros preceding numbers that are non-zero are non-significant as they only define the place of decimal.
• The zeros in between numbers that are non-zero are also significant.
• The zeros after numbers that are non-zero are significant only if the decimal is present in the number.

Interpretation Introduction

(b)

Interpretation:

Whether the statement “ $1\text{cal}$ is equal to $4.184\text{J}$ ” uses an exact number or not should be stated.

Concept introduction:

An exact number is a completely certain number, that is, which can be counted. For example, 1 kilometer has exactly 1000 meter or 1 dozen has 12 number of items, which is also an exact number.

Exact numbers have infinite significant figures and zero error or uncertainty. Example 12 has infinite significant figures but 12.00 has 4 significant figures. To exactly determine the uncertainty in the final answer of measurement, significant figures are calculated.

The rules for counting significant figures will be as follows:

• Numbers that are non-zero are significant figures.
• The zeros preceding numbers that are non-zero are non-significant as they only define the place of decimal.
• The zeros in between numbers that are non-zero are also significant.
• The zeros after numbers that are non-zero are significant only if the decimal is present in the number.

Interpretation Introduction

(c)

Interpretation:

Whether the statement that “Mount Everest has $29035\text{ft}$ ” uses an exact number or not should be stated.

Concept introduction:

An exact number is a completely certain number, that is, which can be counted. For example, 1 kilometer has exactly 1000 meter or 1 dozen has 12 number of items, which is also an exact number.

Exact numbers have infinite significant figures and zero error or uncertainty. Example 12 has infinite significant figures but 12.00 has 4 significant figures. To exactly determine the uncertainty in the final answer of measurement, significant figures are calculated.

The rules for counting significant figures will be as follows:

• Numbers that are non-zero are significant figures.
• The zeros preceding numbers that are non-zero are non-significant as they only define the place of decimal.
• The zeros in between numbers that are non-zero are also significant.
• The zeros after numbers that are non-zero are significant only if the decimal is present in the number.

d)

Interpretation Introduction

Interpretation:

Whether the statement that “the world record for $1\text{mile}$ run is $3\min ,43.13\sec$ ” uses an exact number or not should be stated.

Concept introduction:

An exact number is a completely certain number, that is, which can be counted. For example, 1 kilometer has exactly 1000 meter or 1 dozen has 12 number of items, which is also an exact number.

Exact numbers have infinite significant figures and zero error or uncertainty. Example 12 has infinite significant figures but 12.00 has 4 significant figures. To exactly determine the uncertainty in the final answer of measurement, significant figures are calculated.

The rules for counting significant figures will be as follows:

• Numbers that are non-zero are significant figures.
• The zeros preceding numbers that are non-zero are non-significant as they only define the place of decimal.
• The zeros in between numbers that are non-zero are also significant.
• The zeros after numbers that are non-zero are significant only if the decimal is present in the number.