Chapter SH, Problem 9.5.20EP

To determine

The number $10,471,300$ needs to express in scientific notation.

Answer to Problem 9.5.20EP

The number $10,471,300$ in scientific notation is $1.04713\times {10}^7$ .

Explanation of Solution

Given:

  $10,471,300$

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: $10,471,300$

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

Original number: $10,471,300$

New number: $a=1.04713\times {10}^2$

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

New number: $a=1.04713\times {10}^2$

Decimal count: $b=5$

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

  $\begin{array}{l}10,471,300=a\times {10}^b\\ 10,471,300=1.04713\times {10}^2\times {10}^5\\ 10,471,300=1.04713\times {10}^7\end{array}$

Conclusion:

Hence, $10,471,300=1.04713\times {10}^7$ .