To determine the correct scientific notation of 120 million, let's break down the problem step-by-step.
1. Understand Scientific Notation:
- Scientific notation is a way of expressing numbers that are too large or too small in a compact form.
- A number in scientific notation is written as the product of a number (known as the coefficient) that is between 1 and 10, and a power of 10.
- For example, the number [tex]\(N\)[/tex] in scientific notation is expressed as [tex]\(N = a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
2. Convert 120 Million to Scientific Notation:
- The number 120 million is written numerically as 120,000,000.
- To convert 120,000,000 to scientific notation, we need to move the decimal point to create a coefficient between 1 and 10.
- We move the decimal point 8 places to the left to convert 120,000,000 to 1.2 [tex]\(\times\)[/tex] 10[tex]\(^8\)[/tex].
3. Evaluate the Options:
- Option A: [tex]\(2 \times 10^{-8}\)[/tex]: This notation is incorrect because it represents a very small number, not a large number like 120 million.
- Option B: [tex]\(1.20 \times 10^1\)[/tex]: This notation is incorrect because it is equivalent to 12, which is much smaller than 120 million.
- Option C: [tex]\(1.2 \times 10^7\)[/tex]: This notation represents 12 million (1.2 [tex]\(\times\)[/tex] 10,000,000), which is not equal to 120 million.
- Option D: [tex]\(1.20 \times 10^8\)[/tex]: This notation correctly represents 120 million. The coefficient 1.20 (which is essentially the same as 1.2) multiplied by [tex]\(10^8\)[/tex] gives us 120 million.
4. Conclusion:
- The correct scientific notation for 120 million is [tex]\(1.2 \times 10^8\)[/tex].
Thus, the correct choice among the given options is:
D. [tex]\(1.20 \times 10^8\)[/tex]
