Answer :
To convert the given GDP of Germany in 2008, 26.5 billion, into scientific notation, we'll follow these steps:
1. Identify the Given Value:
The GDP is given as 26.5 billion. Firstly, let's understand what this means in numerical form.
- 1 billion is equal to [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 is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It should have a coefficient between 1 and 10, and a power of 10.
- Here, 26.5 is larger than 10, so we must adjust it to fit the scientific notation format.
- We write [tex]\(26.5\)[/tex] as [tex]\(2.65 \times 10\)[/tex].
- Therefore, [tex]\(26.5 \times 10^9 = 2.65 \times 10 \times 10^9\)[/tex].
3. Combine the Powers of 10:
- Using the rules of exponents, we know that [tex]\(10 \times 10^9 = 10^{10}\)[/tex].
- So, combining these, [tex]\(2.65 \times 10 \times 10^9 = 2.65 \times 10^{10}\)[/tex].
Thus, the scientific notation of 26.5 billion is:
[tex]\[ \boxed{2.65 \cdot 10^{10}} \][/tex]
Therefore, the correct option is:
A. [tex]\(2.65 \cdot 10^{10}\)[/tex]
1. Identify the Given Value:
The GDP is given as 26.5 billion. Firstly, let's understand what this means in numerical form.
- 1 billion is equal to [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 is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It should have a coefficient between 1 and 10, and a power of 10.
- Here, 26.5 is larger than 10, so we must adjust it to fit the scientific notation format.
- We write [tex]\(26.5\)[/tex] as [tex]\(2.65 \times 10\)[/tex].
- Therefore, [tex]\(26.5 \times 10^9 = 2.65 \times 10 \times 10^9\)[/tex].
3. Combine the Powers of 10:
- Using the rules of exponents, we know that [tex]\(10 \times 10^9 = 10^{10}\)[/tex].
- So, combining these, [tex]\(2.65 \times 10 \times 10^9 = 2.65 \times 10^{10}\)[/tex].
Thus, the scientific notation of 26.5 billion is:
[tex]\[ \boxed{2.65 \cdot 10^{10}} \][/tex]
Therefore, the correct option is:
A. [tex]\(2.65 \cdot 10^{10}\)[/tex]
