Final answer:
When comparing a standard penny to a golden penny, the golden penny is slightly heavier (2.6 grams versus 2.5 grams). Significant figures indicate the degree of uncertainty in measurements, which depends on the precision of the measuring device. Thus, the slight difference suggests different materials might be used in the coins.
Step-by-step explanation:
When comparing the mass of a penny to that of a golden penny, we can deduce some facts about their measurements. The standard penny has a mass of 2.498 grams, and this is rounded to 2.5 grams to the nearest tenth of a gram. When we find that a golden penny has a mass of 2.6 grams, this tells us that the golden penny is slightly heavier than the standard penny. This difference might suggest that the two pennies are made from different materials, as gold is denser than the copper alloy typically used in pennies.
Every measurement has some degree of uncertainty, which influences the certainty with which we can conclude that two objects with closely recorded masses are actually different in weight. For example, a scale with a nominal uncertainty in the measurement of ± 0.1 gram would suggest the mass of the golden penny could be anywhere from 2.5 to 2.7 grams.
In measurements, the concept of significant figures is important. Significant figures include all the numbers that are known with certainty plus one final digit that is somewhat uncertain. This uncertainty is determined by the precision of the measuring device used. Hence, when we measure the standard penny at 2.5 grams, the number 2 is certain, and the number 5 in the tenth place is less certain. For the golden penny measured at 2.6 grams, the 2 is certain while the 6 is less certain. The actual difference in mass must consider these uncertainties.