To determine the number of significant figures in the length [tex]\(1.20407 \times 10^{10}\)[/tex] meters, you need to analyze the digit portion before the exponent (i.e., the number [tex]\(1.20407\)[/tex]).
Here are the steps to identify significant figures:
1. Identify all non-zero digits: All non-zero digits are always significant. In [tex]\(1.20407\)[/tex], these are [tex]\(1\)[/tex], [tex]\(2\)[/tex], [tex]\(4\)[/tex], and [tex]\(7\)[/tex].
2. Identify any zeros that are between significant figures: These zeros are also significant. In this number, there are two such zeros between non-zero digits [tex]\(2\)[/tex] and [tex]\(4\)[/tex], making them significant as well.
3. Identify trailing zeros if they are to the right of the decimal point: These zeros are significant only if there is a decimal point explicitly shown. Since [tex]\(1.20407\)[/tex] does show the decimal point, any zeros in between non-zero digits contribute to the significant figures count—but in this case, no trailing zeros exist beyond the decimal point at the end of [tex]\(1.20407\)[/tex].
So, summarizing the significant figures in the number [tex]\(1.20407\)[/tex]:
- Digits [tex]\(1, 2, 0, 4, 0, 7\)[/tex] are all significant.
Therefore, the number of significant figures in [tex]\(1.20407 \times 10^{10}\)[/tex] meters is 6.
