Chapter 4.5, Problem 30IP

a

To determine

To find: abouthow many flashes of lightning are there in a day, write answer in scientific notation and in standard form

Answer to Problem 30IP

There are $8.64\cdot {10}^6$

and 8,640,000 flashes of lightning in a day in scientific notation and in standard form

Explanation of Solution

Given information:

Each minute, there are approximately $6\cdot {10}^3$ flashes of lightning around the world. The air around a lightning bold is heated to about $5.4\cdot {10}^4$ degrees Fahrenheit, which is about five times hotter than the sun.

Calculation:

There are $1440=1.44\cdot {10}^3$ minutes in a day.

Therefore, in 1 minute flashes of lightning $=6\cdot {10}^3$

In $1.44\cdot {10}^3$ minutes flashes of lightning

  $\begin{array}{l}=6\cdot {10}^3\left(1.44\cdot {10}^3\right)\\ =\left(6\cdot 1.44\right)\left({10}^3\cdot {10}^3\right)\\ =8.64\cdot {10}^6\end{array}$

Therefore, there are $8.64\cdot {10}^6$ flashes of lightning in a day.

Hence, there are $8.64\cdot {10}^6$ and 8,640,000 flashes of lightning in a day in scientific notation and in standard form.

b

To determine

To find:about how hot is the sun in degrees Fahrenheit, write answer in scientific notation and in standard form

Answer to Problem 30IP

The sun is hot $1.08\cdot {10}^4$ and 10,800 degrees Fahrenheit in scientific notation and in standard form

Explanation of Solution

Given information:

Each minute, there are approximately $6\cdot {10}^3$ flashes of lightning around the world. The air around a lightning bold is heated to about $5.4\cdot {10}^4$ degrees Fahrenheit, which is about five times hotter than the sun.

Calculation:

The air around a lightning bolt $=5.4\cdot {10}^4$

It is five times hotter than the sun

  $\begin{array}{l}=\frac{5.4\cdot {10}^4}{5}\\ =1.08\cdot {10}^4\end{array}$

Hence,the sun is hot $1.08\cdot {10}^4$ and 10,800 degrees Fahrenheitin scientific notation and in standard form.