To write the GDP of Germany in 2008, which was roughly 26.5 billion, in scientific notation, follow these steps:
1. Understand the Number:
- The number given is 26.5 billion.
- In numerical terms, billion means [tex]\(10^9\)[/tex].
- Therefore, 26.5 billion can be written as [tex]\(26.5 \times 10^9\)[/tex].
2. Convert to Scientific Notation:
- Scientific notation standardizes numbers to a form where there is one non-zero digit to the left of the decimal point followed by [tex]\( \times 10^n \)[/tex].
- For the given number, 26.5 can be rewritten as [tex]\(2.65 \times 10^1\)[/tex], because moving the decimal one place to the left converts it from 26.5 to 2.65.
3. Recalculate Using Exponents:
- Replace the 26.5 with [tex]\(2.65 \times 10^1\)[/tex].
- Hence, when you rewrite 26.5 billion:
[tex]\[
26.5 \times 10^9 = 2.65 \times 10^1 \times 10^9
\][/tex]
4. Combine the Exponents:
- Using the laws of exponents ([tex]\(10^a \times 10^b = 10^{a+b}\)[/tex]):
[tex]\[
2.65 \times 10^1 \times 10^9 = 2.65 \times 10^{1+9} = 2.65 \times 10^{10}
\][/tex]
Therefore, 26.5 billion in scientific notation is:
[tex]\[
2.65 \times 10^{10}
\][/tex]
Given the options, the correct one is:
D. [tex]\(\$2.65 \cdot 10^{10}\)[/tex].
