To determine which decimal has the greatest value, we can compare the given decimals:
1. 0.5:
- This value has a single digit after the decimal point.
2. 0.05:
- This value has two digits after the decimal point.
3. 0.0005:
- This value has four digits after the decimal point.
To compare these values, observe the position and significance of each digit:
- The number 0.5 has a '5' immediately following the decimal point, which represents [tex]\( 5 \times 10^{-1} \)[/tex].
- The number 0.05 has a '5' in the second decimal place, which represents [tex]\( 5 \times 10^{-2} \)[/tex].
- The number 0.0005 has a '5' in the fourth decimal place, which represents [tex]\( 5 \times 10^{-4} \)[/tex].
Clearly, the more significant the position of the digit '5' after the decimal, the larger its value:
- [tex]\( 5 \times 10^{-1} = 0.5 \)[/tex]
- [tex]\( 5 \times 10^{-2} = 0.05 \)[/tex]
- [tex]\( 5 \times 10^{-4} = 0.0005 \)[/tex]
So, comparing these positions, we see that [tex]\( 0.5 \)[/tex] is the largest value, followed by [tex]\( 0.05 \)[/tex] and then [tex]\( 0.0005 \)[/tex].
Therefore, the decimal with the greatest value is:
0.5
