To determine which of the given numbers is the smallest, we will convert each number from its scientific notation (standard form) into a comparable format and then compare them.
Here are the numbers given:
A. [tex]\(7.5 \times 10^{-4}\)[/tex]
B. [tex]\(2.9 \times 10^3\)[/tex]
C. [tex]\(4.5 \times 10^1\)[/tex]
D. [tex]\(3.2 \times 10^{-9}\)[/tex]
Convert each number into decimal form:
A. [tex]\(7.5 \times 10^{-4}\)[/tex]
- This means [tex]\(7.5\)[/tex] times [tex]\(0.0001\)[/tex], which equals [tex]\(0.00075\)[/tex].
B. [tex]\(2.9 \times 10^3\)[/tex]
- This is the same as [tex]\(2.9\)[/tex] times [tex]\(1000\)[/tex], which equals [tex]\(2900\)[/tex].
C. [tex]\(4.5 \times 10^1\)[/tex]
- This is equivalent to [tex]\(4.5\)[/tex] times [tex]\(10\)[/tex], which equals [tex]\(45\)[/tex].
D. [tex]\(3.2 \times 10^{-9}\)[/tex]
- This means [tex]\(3.2\)[/tex] times [tex]\(0.000000001\)[/tex], which equals [tex]\(0.0000000032\)[/tex].
Now, compare the values we have calculated:
- [tex]\(0.00075\)[/tex]
- [tex]\(2900\)[/tex]
- [tex]\(45\)[/tex]
- [tex]\(0.0000000032\)[/tex]
By comparison, the smallest value is:
[tex]\[ 0.0000000032 \][/tex]
Thus, the smallest number among the given options is:
[tex]\[ 3.2 \times 10^{-9} \][/tex]
So, the smallest number is option D.
