Chapter 5.1, Problem 2RQ

(a)

Interpretation Introduction

Interpretation: Scientific notation for 9314 needs to be explained.

Concept Introduction : Scientific notation − For numerical there is long calculation and larger values difficult to use and memorize. Here is the way that scientists easily handle very large numbers or very small numbers with help of scientific notation.

Answer to Problem 2RQ

The scientific notation -

  $=9.314\times {10}^3$

Explanation of Solution

For the scientific notation some basic step follows-

In scientific notation each number is representing as a product of two numbers. The two numbers are multiplied together as - $\text{a}\text{coefficient}{\text{×10}}^{\text{an}\text{exponent}}$

The larger value converted into scientific notation where the decimal point is shifted to that number of places to the right side when a positive exponent is larger.

The sign of exponent is depending on size of the number, number $0$ up to $10$ then negative sign of exponent, number $10$ or greater than $10$ the sign positive of exponent.

For the scientific notation

  $9314$

  $=9.314\times {10}^3$

(b)

Interpretation Introduction

Interpretation: Scientific notation for 0.08042 needs to be determined.

Concept Introduction : Scientific notation − For numerical there is long calculation and larger values difficult to use and memorize. Here is the way that scientists easily handle very large numbers or very small numbers with help of scientific notation.

Answer to Problem 2RQ

The scientific notation -

  $8.042\times {10}^{-2}$

Explanation of Solution

For the scientific notation some basic step follows-

In scientific notation each number is representing as a product of two numbers. The two numbers are multiplied together as - $\text{a}\text{coefficient}{\text{×10}}^{\text{an}\text{exponent}}$

The larger value converted into scientific notation where the decimal point is shifted to that number of places to the right side when a positive exponent is larger.

The sign of exponent is depending on size of the number, number $0$ up to $10$ then negative sign of exponent, number $10$ or greater than $10$ the sign positive of exponent.

For the scientific notation

  $0.08042$

  $=8.042\times {10}^{-2}$

(c)

Interpretation Introduction

Interpretation: Scientific notation for 0.0000517 needs to be determined.

Concept Introduction : Scientific notation − For numerical there is long calculation and larger values difficult to use and memorize. Here is the way that scientists easily handle very large numbers or very small numbers with help of scientific notation.

Answer to Problem 2RQ

The scientific notation -

  $5.17\times {10}^{-5}$

Explanation of Solution

For the scientific notation some basic step follows-

In scientific notation each number is representing as a product of two numbers. The two numbers are multiplied together as - $\text{a}\text{coefficient}{\text{×10}}^{\text{an}\text{exponent}}$

The larger value converted into scientific notation where the decimal point is shifted to that number of places to the right side when a positive exponent is larger.

The sign of exponent is depending on size of the number, number $0$ up to $10$ then negative sign of exponent, number $10$ or greater than $10$ the sign positive of exponent.

For the scientific notation

  $0.0000517$

  $=5.17\times {10}^{-5}$

(d)

Interpretation Introduction

Interpretation: Scientific notation for 7124369582 needs to be explained.

Concept Introduction : Scientific notation − For numerical there is long calculation and larger values difficult to use and memorize. Here is the way that scientists easily handle very large numbers or very small numbers with help of scientific notation.

Answer to Problem 2RQ

The scientific notation -

  $7.124369582\times {10}^9$

Explanation of Solution

For the scientific notation some basic step follows-

In scientific notation each number is representing as a product of two numbers. The two numbers are multiplied together as - $\text{a}\text{coefficient}{\text{×10}}^{\text{an}\text{exponent}}$

The larger value converted into scientific notation where the decimal point is shifted to that number of places to the right side when a positive exponent is larger.

The sign of exponent is depending on size of the number, number $0$ up to $10$ then negative sign of exponent, number $10$ or greater than $10$ the sign positive of exponent.

For the scientific notation

  $7,124,369,582$

  $=7.124369582\times {10}^9$

This can be further rounded off to $7.12\times {10}^9$