Sure, let's go through the steps to convert [tex]\( 450 \times 10^4 \)[/tex] into scientific notation.
1. Identify the given number: [tex]\( 450 \times 10^4 \)[/tex].
2. To convert this number into scientific notation, we need to express it in the form of [tex]\( a \times 10^b \)[/tex] where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
3. First, express 450 in a form that fits our requirements for the coefficient part (a number between 1 and 10):
[tex]\[
450 = 4.5 \times 10^2.
\][/tex]
4. Now, substitute [tex]\( 450 \)[/tex] in the original expression:
[tex]\[
450 \times 10^4 = (4.5 \times 10^2) \times 10^4.
\][/tex]
5. Combine the powers of 10:
[tex]\[
(4.5 \times 10^2) \times 10^4 = 4.5 \times 10^{(2+4)} = 4.5 \times 10^6.
\][/tex]
Thus, the number [tex]\( 450 \times 10^4 \)[/tex] converted into scientific notation is [tex]\( 4.5 \times 10^6 \)[/tex].
- The coefficient, which goes in the green box, is 4.5.
- The exponent, which goes in the yellow box, is 6.
Therefore, the correct scientific notation is:
[tex]\[
\boxed{4.5} \times 10^{\boxed{6}}
\][/tex]
