Chapter A.1, Problem 2E

(a)

Interpretation Introduction

Interpretation:

The usual form has to be given for the given numbers from scientific notation.

Concept introduction:

Scientific notation:

For the given number the scientific notation is given by

$\begin{array}{l}\text{A}\text{×}{\text{10}}^{\text{n}}\\ \text{where,}\\ \text{A}\text{-}\text{a}\text{number}\text{greater}\text{than}\text{or equal to 1 and less than 10}\text{.}\\ \text{n}\text{-}{\text{n}}^{\text{th}}\text{power}\text{of}\text{10}\text{(positive}\text{or}\text{negative}\text{integer)}\text{.}\end{array}$

Here, the value and sign of $\text{n}$ depends on the number of decimal places moved right or left.

$\begin{array}{l}\text{A}\text{×}{\text{10}}^{\text{+n}}\\ \text{if}\text{the}\text{decimal}\text{point}\text{is}\text{moved}\text{to}\text{the}\text{left}\text{.}\\ \text{A}\text{×}{\text{10}}^{\text{-n}}\\ \text{if}\text{the}\text{decimal}\text{point}\text{is}\text{moved}\text{to}\text{the}\text{right}\text{.}\end{array}$

To convert: The given number from scientific notation to usual form

(b)

Interpretation Introduction

Interpretation:

The usual form has to be given for the given numbers from scientific notation.

Concept introduction:

Scientific notation:

For the given number the scientific notation is given by

$\begin{array}{l}\text{A}\text{×}{\text{10}}^{\text{n}}\\ \text{where,}\\ \text{A}\text{-}\text{a}\text{number}\text{greater}\text{than}\text{or equal to 1 and less than 10}\text{.}\\ \text{n}\text{-}{\text{n}}^{\text{th}}\text{power}\text{of}\text{10}\text{(positive}\text{or}\text{negative}\text{integer)}\text{.}\end{array}$

Here, the value and sign of $\text{n}$ depends on the number of decimal places moved right or left.

$\begin{array}{l}\text{A}\text{×}{\text{10}}^{\text{+n}}\\ \text{if}\text{the}\text{decimal}\text{point}\text{is}\text{moved}\text{to}\text{the}\text{left}\text{.}\\ \text{A}\text{×}{\text{10}}^{\text{-n}}\\ \text{if}\text{the}\text{decimal}\text{point}\text{is}\text{moved}\text{to}\text{the}\text{right}\text{.}\end{array}$

To convert: The given number from scientific notation to usual form