To determine which measurement has five significant figures, let's analyze each given value step by step. Here are the rules for counting significant figures:
1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros are not significant.
4. Trailing zeros in a number containing a decimal point are significant.
5. Trailing zeros in a whole number with no decimal point are not significant.
Using these rules:
1. 0.275:
- This number has three non-zero digits and no zeros.
- Significant figures: 3
2. 750:
- This number has two non-zero digits and one trailing zero in a whole number with no decimal point.
- Significant figures: 2 (zeros are not significant here)
3. [tex]$10.4 \times 10^5$[/tex]:
- This number is in scientific notation and the coefficient 10.4 has three significant digits (the zeros between non-zero digits are included).
- Significant figures: 3
4. 11,890:
- This number has five digits, with four non-zero digits and one trailing zero in a whole number.
- Significant figures: 5 (the zero between non-zero digits and trailing zero are significant)
5. 320,050:
- This number has six digits with four non-zero digits and two zeros, one between non-zero digits and one trailing zero.
- Significant figures: 5 (the zero between non-zero digits is significant, and the trailing zero is also significant because there is an implied decimal point)
Given the analysis:
- 0.275 has 3 significant figures
- 750 has 2 significant figures
- [tex]$10.4 \times 10^5$[/tex] has 3 significant figures
- 11,890 has 5 significant figures
- 320,050 has 5 significant figures
So, the measurements that have five significant figures are 11,890 and 320,050.
Given the options provided:
A. 750 (2 significant figures)
B. 11,890 (5 significant figures)
C. 320,050 (5 significant figures)
D. [tex]$10.4 \times 10^5$[/tex] (3 significant figures)
Both B and C are correct, but since there is no direct clue about multiple correct answers in the options, we might consider the first matching option:
B. 11,890
Therefore, the correct answer is:
B. 11,890
