Chapter 2, Problem 72A

(a)

Interpretation Introduction

Interpretation:

The given number needs to be converted into scientific notation if each X represents a significant figure.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does not express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 72A

The given number in scientific notation will be $\text{X}\text{. XXXX}\times {10}^2$.

Explanation of Solution

In the given number, the decimal point moved two places to the left which means that the $10$ will be raised to a power of two positive. All the values in the given number are significant i.e 5. Hence, the given number in scientific notation will be $\text{X}\text{. XXXX}\times {10}^2$

(b)

Interpretation Introduction

The given number needs to be written in scientific notation if each X represents a significant figure.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 72A

The given number in scientific notation will be $\text{X}\text{. XX}\times {10}^{-7}$.

Explanation of Solution

In the given number, the decimal point moved seven places to the right which means that the $10$ will be raised to a power of seven negative. All the values in the given number are significant i.e 3. Hence, the given number in scientific notation will be $\text{X}\text{. XX}\times {10}^{-7}$