Answer :
To determine which number corresponds to the scientific notation [tex]\(8.0007 \cdot 10^6\)[/tex], let's follow a step-by-step process to convert the scientific notation to standard form.
1. Understand Scientific Notation:
- Scientific notation expresses numbers as a product of a coefficient (a number between 1 and 10) and a power of 10.
- Here, the coefficient is [tex]\(8.0007\)[/tex] and the power of 10 is [tex]\(10^6\)[/tex].
2. Express the Power of 10:
- [tex]\(10^6\)[/tex] means [tex]\(1\)[/tex] followed by [tex]\(6\)[/tex] zeros, or [tex]\(1,000,000\)[/tex].
3. Multiply the Coefficient by [tex]\(10^6\)[/tex]:
- To convert [tex]\(8.0007 \cdot 10^6\)[/tex] to standard form, we multiply [tex]\(8.0007\)[/tex] by [tex]\(10^6\)[/tex].
- This involves moving the decimal point in [tex]\(8.0007\)[/tex] six places to the right.
4. Shift the Decimal Point:
- Starting with [tex]\(8.0007\)[/tex]:
- Move the decimal point six places to the right:
[tex]\(8.0007 \rightarrow 80,007.0 \rightarrow 800,070.0 \rightarrow 8,000,700.0\)[/tex]
5. Standard Form Result:
- After moving the decimal point six places to the right, we get [tex]\(8,000,700\)[/tex].
Now, let's match this number with the given options:
[tex]\[ \begin{align*} A. & \ 80,007,000 \\ B. & \ 80,000,700 \\ C. & \ 8,000,700 \\ D. & \ 8,007,000 \\ \end{align*} \][/tex]
The number [tex]\(8,000,700\)[/tex] corresponds to option C.
Therefore, the correct answer is:
C. [tex]\(8,000,700\)[/tex]
1. Understand Scientific Notation:
- Scientific notation expresses numbers as a product of a coefficient (a number between 1 and 10) and a power of 10.
- Here, the coefficient is [tex]\(8.0007\)[/tex] and the power of 10 is [tex]\(10^6\)[/tex].
2. Express the Power of 10:
- [tex]\(10^6\)[/tex] means [tex]\(1\)[/tex] followed by [tex]\(6\)[/tex] zeros, or [tex]\(1,000,000\)[/tex].
3. Multiply the Coefficient by [tex]\(10^6\)[/tex]:
- To convert [tex]\(8.0007 \cdot 10^6\)[/tex] to standard form, we multiply [tex]\(8.0007\)[/tex] by [tex]\(10^6\)[/tex].
- This involves moving the decimal point in [tex]\(8.0007\)[/tex] six places to the right.
4. Shift the Decimal Point:
- Starting with [tex]\(8.0007\)[/tex]:
- Move the decimal point six places to the right:
[tex]\(8.0007 \rightarrow 80,007.0 \rightarrow 800,070.0 \rightarrow 8,000,700.0\)[/tex]
5. Standard Form Result:
- After moving the decimal point six places to the right, we get [tex]\(8,000,700\)[/tex].
Now, let's match this number with the given options:
[tex]\[ \begin{align*} A. & \ 80,007,000 \\ B. & \ 80,000,700 \\ C. & \ 8,000,700 \\ D. & \ 8,007,000 \\ \end{align*} \][/tex]
The number [tex]\(8,000,700\)[/tex] corresponds to option C.
Therefore, the correct answer is:
C. [tex]\(8,000,700\)[/tex]
