The GDP of Germany in 2008 was roughly 26.5 billion. How do you write this in scientific notation?

A. [tex]26.5 \cdot 10^8[/tex]
B. [tex]2.65 \cdot 10^9[/tex]
C. [tex]26.5 \cdot 10^9[/tex]
D. [tex]2.65 \cdot 10^{10}[/tex]



Answer :

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].