Chapter 3, Problem 63A

Interpretation Introduction

Interpretation : The given units are to be ordered and expressed in terms of meters.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor.

Answer to Problem 63A

The order of units from smallest to largest: $\text{pm}$ , $\text{nm}$ , $\text{μm}$ , $\text{mm}$ , $\text{cm}$ , $\text{dm}$ , $\text{m}$ and $\text{km}$ .

The measurement in terms of meters is given as:

  $\begin{array}{l}\text{1}\text{cm}\text{=}{\text{10}}^{-\text{2}}\text{m}\\ \text{1}\text{μm}\text{=}{10}^{-6}\text{m}\\ \text{1km}={10}^3\text{m}\\ \text{1mm}\text{=}{\text{10}}^{-3}\text{m}\end{array}$

  $\begin{array}{l}\text{1}\text{m}\text{=}\text{1}\text{m}\\ \text{1}\text{nm}\text{=}{10}^{-9}\text{m}\\ \text{1dm}={10}^{-1}\text{m}\\ \text{1pm}\text{=}{\text{10}}^{-12}\text{m}\end{array}$

Explanation of Solution

An equivalent measurement ratio is referred to as a conversion factor.

All the given units are units of length.

To find the order of the units, relate the units to meter.

The units such as centimeter, micrometer, kilometer, and millimeter are expressed as

  $\begin{array}{l}\text{1}\text{cm}\text{=}{\text{10}}^{-\text{2}}\text{m}\\ \text{1}\text{μm}\text{=}{10}^{-6}\text{m}\\ \text{1km}={10}^3\text{m}\\ \text{1mm}\text{=}{\text{10}}^{-3}\text{m}\end{array}$

Similarly, the units such as meter, nanometer, decimeter and picometer are expressed as

  $\begin{array}{l}\text{1}\text{m}\text{=}\text{1}\text{m}\\ \text{1}\text{nm}\text{=}{10}^{-9}\text{m}\\ \text{1dm}={10}^{-1}\text{m}\\ \text{1pm}\text{=}{\text{10}}^{-12}\text{m}\end{array}$

From the expressions, the order of the units was found.

The order of units from smallest to largest: $\text{pm}$ , $\text{nm}$ , $\text{μm}$ , $\text{mm}$ , $\text{cm}$ , $\text{dm}$ , $\text{m}$ and $\text{km}$ .