Chapter 8.8, Problem 34E

To determine

To write:

The given number in scientific notation.

Answer to Problem 34E

Our given number in scientific notation would be $5.0\times {10}^{-4}$ .

Explanation of Solution

Given:

A number:

  $0.0005$ .

Concept used:

To convert a number into scientific notation, we write the given number as product of two numbers. One factor is a number between 1 and 10, while the 2^nd factor is power of 10.

When a decimal is to the right of given number, then we need to move the decimal to left such that the number gets between 1 and 10. Then, we multiply the number by power of 10 that many times, we moved the decimal to left.

When a decimal is to the left of given number, then we need to move the decimal to right such that the number gets between 1 and 10. Then, we multiply the number by negative power of 10 that many times, we moved the decimal to right.

Calculation:

To write our given number, we will shift the decimal to right by 4 units. To shift the decimal, we will multiply our number by ${10}^{-4}$ to keep the value of number same.

  $0.0005=5.0\times {10}^{-4}$

Therefore, our given number in scientific notation would be $5.0\times {10}^{-4}$ .