Final answer:
The assertion regarding the length of decimal numbers does not provide evidence for their comparative size. Decimals must be compared place by place, and in the case of 0.196 and 0.15, 0.196 is larger because of the value in the hundredths place.
Step-by-step explanation:
No, the student's claim that "0.196 is bigger than 0.15 because if it is three numbers long, it will always be bigger than if it is two numbers long" is incorrect and does not provide evidence for why 0.196 is greater than 0.15. When comparing decimal numbers, the number of digits is not important; rather, you should compare the numbers place by place. In this case, if we compare 0.196 and 0.15, we start by comparing the digits in the tenths place: 1 is the same in both numbers. Next, we compare the hundredths place: 9 in 0.196 is larger than 5 in 0.15. Therefore, without needing to consider the thousandths place, we can already conclude that 0.196 is larger than 0.15.
To reinforce the concept, when considering significant figures, an important topic in measurements, the number of digits can give us an indication of precision, but it's not simply the length of the number that matters. For example, in the measurement of 150 mm, the significance of the zero depends on the precision of the measuring instrument. The length of a number alone does not determine its value.