What is the difference between the measured values of 1.05m and 1.050m? What factor of a measurement tool determines the sig figs of a measured value?

The two values are different because of their sig figs, the first has 3 and the other has 4. I think that the factor of a measurement tool that determines the sig figs is the least count.

Are my answers correct? Thank you!

If it was 1.0500000m, would there be eight significant figures?

Yes, you are correct!

The difference between the measured values of 1.05m and 1.050m lies in the number of significant figures (sig figs). The first value, 1.05m, has three sig figs, while the second value, 1.050m, has four sig figs.

Sig figs are important because they indicate the precision or level of certainty in a measurement. The more sig figs a measurement has, the more precise the measurement is considered to be.

Now, regarding your question about the factor that determines the sig figs of a measured value, you are right that it is the least count of the measurement tool. The least count, also known as the smallest division or smallest increment, is the smallest unit that the measurement tool can detect or measure. The least count plays a crucial role in determining the level of precision and the number of significant figures in a measurement.

To determine the sig figs of a measured value, you count the number of digits starting from the first non-zero digit, then continue until the last digit that represents a valid measurement based on the least count. Trailing zeroes after the last non-zero digit and without any other non-zero digit in between are considered significant in a measured value.

So, in your example, if the least count of the measurement tool used was 0.001m (1 millimeter), then both 1.05m and 1.050m have three significant figures because the last zero in both values provides additional precision within the least count. However, if the least count was 0.01m (1 centimeter), then 1.05m would have two significant figures and 1.050m would have three significant figures because the last zero in 1.05m is not providing additional precision within the least count.

Remember, the significant figures in a measurement depend on the precision and limitations of the measurement tool used, specifically the least count.

Your answer is partially correct.

The difference between the measured values of 1.05m and 1.050m is indeed due to the significant figures. The first value has three significant figures, while the second value has four significant figures.

However, the factor of a measurement tool that determines the significant figures of a measured value is not the least count. The least count is the smallest measurement that a measurement tool can make. For example, if a ruler has a least count of 0.1cm, it means that it can measure lengths to the nearest 0.1cm.

The significant figures of a measured value depend on the precision of the measurement tool used. Generally, the rule is that all certain digits and the first uncertain digit are considered as significant figures. Uncertain digits are those that have been estimated or are beyond the capability of the instrument to measure accurately.

So, the factor that determines the significant figures of a measured value is the precision of the measurement tool, not the least count.