To determine the number of significant digits in the given number [tex]\(0.030100 \times 10^3\)[/tex], we need to consider the rules for counting significant figures:
1. All non-zero digits are significant.
2. Any zeros between nonzero digits are significant.
3. Leading zeros (zeros to the left of the first non-zero digit) are not significant.
4. Trailing zeros in a number containing a decimal point are significant.
Following these rules, let's break down the number:
1. Convert the number to its decimal form:
[tex]\[ 0.030100 \times 10^3 \][/tex]
[tex]\[
0.030100 \times 10^3 = 30.100
\][/tex]
2. Identify the significant digits in the number 30.100:
- The digit '3' is significant.
- The digit '0' between '3' and '1' is significant.
- The digit '1' is significant.
- The trailing zeros after the decimal point ('00') are significant because there is a decimal point present.
Therefore, the significant digits in 30.100 are: 3, 0, 1, 0, and 0.
Thus, the total number of significant digits in [tex]\(0.030100 \times 10^3\)[/tex] is 5.
