- #1

Cardinalmont

Gold Member

- 22

- 3

## Main Question or Discussion Point

There is something I seriously don't understand about uncertainty.

Suppose there is an electric balance that reads 5.67g

The limit of reading is 0.01g

The greatest possible error is half of the limit of reading and is thus 0.005g

By this logic, and assuming the very best possible situation, I would think one could record the mass of the coin as (5.67±0.005)g.

This makes sense to me because the scale shows 5.67g, but the actual mass of the coin can be anywhere from 5.665 to 5.675 and the scale had to round the number to just 2 decimal places.

The problem with the way I understand it is that a quantity's uncertainty is limited by the decimal place of the quantity. If 5.67 ends in the hundredths so must the 0.005, turning it into 0.01, thus ruining the logic established in the previous paragraph.

Help me please!

Suppose there is an electric balance that reads 5.67g

The limit of reading is 0.01g

The greatest possible error is half of the limit of reading and is thus 0.005g

By this logic, and assuming the very best possible situation, I would think one could record the mass of the coin as (5.67±0.005)g.

This makes sense to me because the scale shows 5.67g, but the actual mass of the coin can be anywhere from 5.665 to 5.675 and the scale had to round the number to just 2 decimal places.

The problem with the way I understand it is that a quantity's uncertainty is limited by the decimal place of the quantity. If 5.67 ends in the hundredths so must the 0.005, turning it into 0.01, thus ruining the logic established in the previous paragraph.

Help me please!