Final answer:
Option a) correctly ranks the values by significant figures: 10.5250g (6 sf), 1.07429g² (7 sf), 3.12200g (6 sf), 0.133788g (6 sf), 0.138557g (6 sf). The other options do not correctly respond to the student's question.
Step-by-step explanation:
The question involves ranking different values based on the number of significant figures (sf) present in each measurement. After analyzing the given options:
- 10.5250g has 6 significant figures. All the digits including the trailing zeroes after the decimal are counted.
- 1.07429g² has 7 significant figures. The squares do not affect counting the significant figures; all non-zero digits and zeroes that are between significant figures or at the end of a number with a decimal are counted.
- 3.12200g has 6 significant figures. The trailing zeros after the decimal point are counted because they indicate precision.
- 0.133788g has 6 significant figures. In this case, there are no trailing zeros, but all non-zero digits are significant.
- 0.138557g has 6 significant figures for the same reason as the previous number.
Thus, option a) correctly ranks the values by significant figures: 10.5250g (6 sf), 1.07429g² (7 sf), 3.12200g (6 sf), 0.133788g (6 sf), 0.138557g (6 sf).
Option b) has different measurements than what was asked in regards to the mass (4.5250g instead of 10.5250g, etc.), so it doesn't directly answer the student's question.
With the corrected counts, we can determine that option c) 'both a and b' cannot be correct, as option b) contains errors, and option d) 'none of the above' is incorrect since option a) does contain the correct ranking of significant figures.