To determine which number is three hundred thousand times larger than [tex]\(1.6 \times 10^2\)[/tex], we will follow these steps:
1. Start with the given number: [tex]\(1.6 \times 10^2\)[/tex].
2. Understand that multiplying by three hundred thousand ([tex]\( 3 \times 10^5 \)[/tex]) involves multiplying this coefficient directly by the numerical value of 300,000.
3. Calculate:
[tex]\[
(1.6 \times 10^2) \times (3 \times 10^5)
\][/tex]
4. Separate the coefficients and the powers of ten:
[tex]\[
1.6 \times 3 = 4.8
\][/tex]
and
[tex]\[
10^2 \times 10^5 = 10^{2+5} = 10^7
\][/tex]
5. Combine the results:
[tex]\[
4.8 \times 10^7
\][/tex]
Thus, the number that is three hundred thousand times larger than [tex]\(1.6 \times 10^2\)[/tex] is:
[tex]\[
\boxed{4.8 \times 10^7}
\][/tex]
