To determine the number of significant figures in the measurement [tex]\(16.400 \, g\)[/tex], we need to follow the rules for identifying significant figures. Here are the steps:
1. All non-zero digits are considered significant:
- In the number [tex]\(16.400\)[/tex], the digits [tex]\(1\)[/tex] and [tex]\(6\)[/tex] are non-zero and hence significant.
2. Any zeros between significant figures are also significant:
- In the number [tex]\(16.400\)[/tex], there is a zero between the significant digit [tex]\(6\)[/tex] and the significant digits following the decimal point, making it significant.
3. Trailing zeros in the decimal part are significant:
- In [tex]\(16.400\)[/tex], the zeros after the decimal point and after the digit [tex]\(4\)[/tex] are significant because they indicate the precision of the measurement.
Combining all the significant figures from the steps above, we have:
- The digits [tex]\(1\)[/tex] and [tex]\(6\)[/tex] (non-zero, hence significant),
- The zero between [tex]\(6\)[/tex] and the decimal point (between significant figures, hence significant),
- The zeros after the decimal point and after the digit [tex]\(4\)[/tex] (trailing zeros in the decimal part, hence significant).
Thus, the measurement [tex]\(16.400 \, g\)[/tex] contains a total of 5 significant figures.
