Chapter SH, Problem 9.5.17EP

To determine

The number $500,300,100$ needs to express in scientific notation.

Answer to Problem 9.5.17EP

The number $500,300,100$ in scientific notation is $5.003001\times {10}^8$ .

Explanation of Solution

Given:

  $500,300,100$

Concept Used:

To write the very large or very small numbers easily, the scientific notation is used. When any number between $1$ and $10$ which is multiplied with the power of $10$ then the scientific notations are in use.

The formula used to reconstruct the number into scientific notation is:

  $SN=a\times {10}^b$

Where,

New number: $a$

Decimal count: $b$

Calculation:

The given number is: $500,300,100$

Take the given number and move a decimal place to the right one position. Get that:

Original number: $500,300,100$

New number: $a=5.003001\times {10}^2$

Need to count the number of places on the right decimal place.

New number: $a=5.003001\times {10}^2$

Decimal count: $b=6$

Now, reconstruct the number by using the formula of scientific notation:

  $\begin{array}{l}500,300,100=a\times {10}^b\\ 500,300,100=5.003001\times {10}^2\times {10}^6\\ 500,300,100=5.003001\times {10}^8\end{array}$

Conclusion:

Hence, $500,300,100=5.003001\times {10}^8$ .