inplied uncertainty?

Question

i have a lab physic started on tuesday and i have read the lab instruction before the lab starting i dont quite understand implied uncertainty

here is a question

1.23 cm have 3 ( place accuracy) ........ +/- .005 ( implied C)
108.7 cm ...... 4 ........................................+/- .05cm
45,000 people...........2..............................+/- 500 people

my question is , how do you figure out implied uncertainty , can you explain to me please help me out
i am appreciated any participates

1.23 has 3 sig fig, then implied uncertainty is 3 from the decimal point to the right that means +/- .005

but 108.7 is 4 sig fig why implied is +/- .05
i think that will be +/- .0005, can you explain more for me please??/

Answer 1

here is the answer
take a look on 1.23 you can see we have 2 digits from decimal place to the right,
the zero on implied uncertainty is determined by the 2 digits and number 5
i meant like: 2 digits so implied will have 2 zero and number 5
+/- .005

108.7 is 1digit so implied will have 1 zero
+/. 05

Answer 2

The key is to identify the number of significant digits. In the first two examples, some digits are given to the right of the decimal point, and this implies that all of these are significant. In the last example, the zeroes may be significant -- or not; the people could have been counted entering the ball park, or simply estimated as being present at a rally.

Answer 3

In Physics, every measurement is just an approximation. Some more approximate than others. Part of doing good science is knowing how approximate your measurement technique is when recording data. This is called "measurement uncertainty."

Unless specified otherwise, data produced by measurement are always assumed to have an uncertainty of half the value of their least significant digit. It doesn't matter which side of the decimal place that digit lies. Functionally what that means is that you have a range of values that would all produce the same measured number.

In your specific examples, it would go like this:

1.23 +/- 0.005 cm means the "actual" value lies somewhere between 1.225 and 1.235 cm
108.7 +/- 0.05 cm = between 108.65 and 108.75 cm
45,000 +/- 500 people = between 44,500 and 45,500 people

If you were measuring time, and got a value of 15 sec, you would record it as 15 +/- 0.5 sec, which means "somewhere between 14.5 and 15.5 seconds"