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Answer :
To express the number 3,760,000,000 in scientific notation, you need to follow these steps:
1. Identify the Significant Figures: Focus on the non-zero digits in the number. Here, the significant figures are "3.76".
2. Positioning the Decimal: Place the decimal point right after the first significant figure. For this number, it becomes "3.76".
3. Counting the Places: Count how many places you move the decimal point from its original position (at the end of the number, as in 3,760,000,000) to the new position (after the 3). This gives the exponent of 10 in the scientific notation.
- Start from the end of the number: 3,760,000,000.
- Move the decimal point to after the first digit: 3.76.
- Count the locations you moved the decimal place: In this case, you move 9 places.
4. Write in Scientific Notation: Combine the significant figures with the power of ten. Since you moved the decimal 9 places, the power of ten will be 9. This gives us:
[tex]\[
3.76 \cdot 10^9
\][/tex]
By following these steps, we confirm that the number 3,760,000,000 expressed in scientific notation is [tex]\(3.76 \cdot 10^9\)[/tex].
Thus, the correct choice is:
D. [tex]\(3.76 \cdot 10^9\)[/tex].
1. Identify the Significant Figures: Focus on the non-zero digits in the number. Here, the significant figures are "3.76".
2. Positioning the Decimal: Place the decimal point right after the first significant figure. For this number, it becomes "3.76".
3. Counting the Places: Count how many places you move the decimal point from its original position (at the end of the number, as in 3,760,000,000) to the new position (after the 3). This gives the exponent of 10 in the scientific notation.
- Start from the end of the number: 3,760,000,000.
- Move the decimal point to after the first digit: 3.76.
- Count the locations you moved the decimal place: In this case, you move 9 places.
4. Write in Scientific Notation: Combine the significant figures with the power of ten. Since you moved the decimal 9 places, the power of ten will be 9. This gives us:
[tex]\[
3.76 \cdot 10^9
\][/tex]
By following these steps, we confirm that the number 3,760,000,000 expressed in scientific notation is [tex]\(3.76 \cdot 10^9\)[/tex].
Thus, the correct choice is:
D. [tex]\(3.76 \cdot 10^9\)[/tex].
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