To write the number 0.0005 in scientific notation, we need to follow these steps:
1. Identify the significant figure:
The number 0.0005 contains one significant figure, which is 5.
2. Determine the exponent by moving the decimal point:
We need to move the decimal point to the right so that only one non-zero digit (5) is to the left of the decimal point. This process helps us identify the exponent of 10.
Starting from 0.0005, we move the decimal point 4 places to the right to place it after the 5:
- Initial position: 0.0005
- After 1 move: 0.005
- After 2 moves: 0.05
- After 3 moves: 0.5
- After 4 moves: 5.
Thus, the number of moves needed is 4, and since we are moving the decimal point to the right, the exponent will be negative. The exponent is -4.
3. Express the number in the correct format:
The scientific notation format is [tex]\( a \times 10^n \)[/tex], where [tex]\( a \)[/tex] is the significant figure and [tex]\( n \)[/tex] is the exponent.
Therefore, 0.0005 in scientific notation is written as [tex]\( 5.0 \times 10^{-4} \)[/tex].
Given the options:
- [tex]\( 5 \times 10^{-4} \)[/tex]
- [tex]\( 5 \times 10^{-3} \)[/tex]
- [tex]\( 5 \times 10^3 \)[/tex]
- [tex]\( 5 \times 10^4 \)[/tex]
The correct answer is:
[tex]\[ 5 \times 10^{-4} \][/tex]
