To determine which number is 30 times larger than [tex]\( 3 \times 10^4 \)[/tex], let's go through the steps.
1. Calculate the Value:
The given number is [tex]\( 3 \times 10^4 \)[/tex].
2. Multiply the Given Number by 30:
We need to find 30 times the given number:
[tex]\( 30 \times (3 \times 10^4) \)[/tex].
3. Simplify the Expression:
Using the associative property of multiplication:
[tex]\( 30 \times 3 \times 10^4 \)[/tex].
4. Perform the Multiplication:
Calculate [tex]\( 30 \times 3 \)[/tex]:
[tex]\( 30 \times 3 = 90 \)[/tex].
So, the expression now becomes [tex]\( 90 \times 10^4 \)[/tex].
5. Express in Scientific Notation:
[tex]\( 90 \times 10^4 \)[/tex] can be written as [tex]\( 9 \times 10^5 \)[/tex] because:
[tex]\( 90 = 9 \times 10 \)[/tex],
hence [tex]\( 90 \times 10^4 = 9 \times 10 \times 10^4 = 9 \times 10^{4+1} = 9 \times 10^5 \)[/tex].
6. Find the Corresponding Option:
Now, let's compare the result with the given options:
- A. [tex]\( 3 \times 10^{90} \)[/tex]
- B. [tex]\( 9 \times 10^5 \)[/tex]
- C. [tex]\( 3 \times 10^{34} \)[/tex]
- D. [tex]\( 9 \times 10^4 \)[/tex]
From the calculation, [tex]\( 30 \times (3 \times 10^4) = 9 \times 10^5 \)[/tex].
Therefore, the correct choice is:
[tex]\[ \boxed{B} \][/tex]
