Question

exercises
complete the following table:

number	# of sf	do the number of sf match the example to the left? (circle yes or no, and explain)
0.23060	5	yes (no. the numbers after the decimal matter)
5.670×10¹⁰	3	yes. (no)
5000.00	5	yes. (no)

problems

1. if you were to weigh a handful of 14 marbles and the entire lot weighed 17.3 g, what would each marble weigh? as a group, decide how many decimal places you should report in your answer.

answer 1.2357 g

1. discuss as a group and explain why you decided on that number of decimal places. use grammatically correct sentences.
2. do you think that there should be a standard number of decimal places reported in answers to problems? how would this benefit/harm science as a whole? discuss this as a group and explain. use grammatically correct sentences.

Explanation:

Problem 1

Step1: Calculate weight per marble

To find the weight of each marble, divide the total weight by the number of marbles. The total weight of 14 marbles is 17.3 g. So the weight of each marble is $17.3\div14=\frac{17.3}{14}\approx1.2357$ g.

Problem 2

The number of decimal - places is chosen based on the precision of the given data. The total weight 17.3 g has one decimal place. When dividing, we can keep more decimal places initially for accuracy in intermediate calculations, but the final answer should be reported with an appropriate number of significant figures. Since 17.3 has 3 significant figures and 14 is an exact number (counting marbles), we can report the answer to 4 significant figures (1.236 g considering rounding rules) which is consistent with the precision of the measured value (17.3 g).

Problem 3

A standard number of decimal places in scientific answers can have both benefits and drawbacks. Benefits: It can improve consistency in reporting data, making it easier to compare results between different experiments and researchers. It can also reduce confusion caused by inconsistent reporting. Drawbacks: Enforcing a strict standard may limit the ability to report very precise or very imprecise measurements accurately. For example, in some cases where high - precision measurements are made, a standard number of decimal places may not be sufficient to convey the true precision of the measurement, and in other cases, overly precise reporting may give a false sense of accuracy for less precise measurements.

Answer:

1. 1.236 g (rounded to 4 significant figures)
2. The answer is reported to 4 significant figures to be consistent with the precision of the measured value (17.3 g which has 3 significant figures) and considering rounding rules. Also, 14 is an exact number.
3. Benefits: Consistency in data reporting, easier comparison of results, reduced confusion. Drawbacks: May limit accurate reporting of highly precise or imprecise measurements, can give a false sense of accuracy in some cases.