To convert the given number [tex]\(14,200,000\)[/tex] into scientific notation, we need to follow these detailed steps:
1. Identify the significant figures: In the number [tex]\(14,200,000\)[/tex], the significant figures are [tex]\(1.42\)[/tex].
2. Determine the power of 10: To express the number [tex]\(14,200,000\)[/tex] in the form [tex]\(1.42 \times 10^n\)[/tex]:
- Move the decimal point in [tex]\(14,200,000\)[/tex] to the position immediately after the first non-zero digit. This gives us [tex]\(1.42\)[/tex].
- Count the number of decimal places the point has moved. Starting from the end of the number (the rightmost digit), we move the decimal point 7 places to the left to position it after the digit 1.
3. Combine the significant figures with the power of 10: Since we moved the decimal point 7 places, we multiply our significant figure [tex]\(1.42\)[/tex] by [tex]\(10^7\)[/tex].
Therefore, the number [tex]\(14,200,000\)[/tex] written in scientific notation is [tex]\(1.42 \times 10^7\)[/tex].
Among the given choices:
- A. [tex]\(1.42 \times 10^6\)[/tex] is incorrect as the exponent is 6 instead of 7.
- B. [tex]\(1.42 \times 10^7\)[/tex] is correct as it matches our result.
- C. [tex]\(142 \times 10^7\)[/tex] is incorrect because it is not in proper scientific notation and represents a different value.
- D. [tex]\(142 \times 1,000,000\)[/tex] is another way to express the number but not in scientific notation form.
Thus, the best answer is:
B. [tex]\(1.42 \times 10^7\)[/tex].
