Chapter 1, Problem 1.88SP

Interpretation Introduction

(a)

Interpretation:

The building with volume $3666500{\text{m}}^{\text{3}}$ is to be represented in 4 and then 2 significant figures.

Concept introduction:

An exact number is a completely certain number, that is, which can be counted. For example, 1 kilometer has exactly 1000 meters 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:

The building with volume $3666500{\text{m}}^{\text{3}}$ is to be represented in scientific notation post-conversion into 4 and 2 significant figures.

Concept introduction:

The size of the units on any system of measurement can be inconveniently very large or small. To solve this problem, SI units are modified by using some appropriate prefixes that are placed before the units to signify how small or big the size of the unit is. For example, the prefix milli is used to represent one-thousandth of 1 meter.

Similarly, numbers that are too large or too small are represented by an exponential format called scientific notations for convenience.

Scientific notations are generally expressed as follows:

$\text{m}{\text{×10}}^{\text{n}}$

Where,

• n is the number of places the decimal has moved and is known as an exponent.
• m is the number.

An example is 55000 is represented as $5.5\times {10}^4$.