Chapter SR8, Problem 12P

Solution

To write the number $0.000000009$ in scientific notation.

  $9\times 10^{-9}$

Given:

The number $0.000000009$ .

Concept Used:

To write a number in scientific notation, move the decimal point after the first nonzero integer and raise the exponent of 10 by the number of digits we moved the decimal point.

If the decimal point was moved to the left, then raise the positive exponent and if the decimal point moved to the right, then raise the negative exponent.

Calculation:

In order to write the number $0.000000009$ in scientific notation, move the decimal 9 digits right next to the first nonzero number and raise the exponent over 10 by $-9$ as shown below

  $\begin{array}{c}0.000000009=9.0\times 10^{-9}\\ =9\times 10^{-9}\end{array}$

Thus, the given number in scientific notation is $9\times 10^{-9}$ .