Significant Figures difficulty

[temaire]

Homework Statement

A newspaper reported an attendance of 15,000. If you assume that this number contains two significant figures, how many people could actually have been at the game?

The Attempt at a Solution

I'm having difficulty answering this problem not because I don't know how to use significant figures, but why we use significant figures. My prof says that since 15000 can be represented as $$1.5 x 10^4$$ the number of people in attendance would range from $$1.4 x 10^4$$ to $$1.6 x 10^4$$. Could someone please explain this to me?

 

[mgb_phys]

If it says 15,000 then rounding off to the nearest 1000 means there was between 14,500 and 15,500.

Using normal numbers eg 15,000 you don't know if they mean 15,000 to the nearest 1000 or the nearest 1, ie 15,000 rather than 15,001
By using scientific notation we can show how many of the 0 are significant.

So 1.5x10^4 (2sig figures) would mean between 1.45x10^4 (14,500) and 1.55x10^4 (15,500) while 1.5000x10^4 (5 sig fig) would mean exactly 15,000

 

[tomcue]

As a scientist, it is important to understand the concept of significant figures and why they are used in scientific calculations. Significant figures represent the precision or accuracy of a measurement. In this case, the reported attendance of 15,000 is assumed to have two significant figures, meaning that the actual number of people in attendance could range from 14,500 to 15,500. This is because the last digit in a number with two significant figures is considered uncertain and can vary by ±1. Therefore, it is important to use significant figures in calculations to ensure that the final result is not reported with more precision than the original data. In this case, the final result should also be reported with two significant figures, resulting in a range of 1.4 x 10^4 to 1.6 x 10^4 people in attendance. This helps to avoid misleading or inaccurate results and maintain the appropriate level of precision in scientific data.