How Should Uncertainties Be Represented When Significant Figures Differ?

[nrslmz]

Homework Statement

When doing operations with numbers with uncertainties, if the significant figures of the resultant number's uncertainty is lower the significant figures of the resultant number, how should I show the resultant uncertainty. For example,

Homework Equations

if you do the operation 5.40+-0.10 / 90.00+-0.05 , the result is
0.06+-0.001

The Attempt at a Solution

the solution must either be
0.06 +- 0.00

or

0.06 +- 0.01x(10^(-1))

since the number of the significant numbers should be equal. so which one is it?

 

[HallsofIvy]

Homework Statement

When doing operations with numbers with uncertainties, if the significant figures of the resultant number's uncertainty is lower the significant figures of the resultant number, how should I show the resultant uncertainty. For example,

Homework Equations

if you do the operation 5.40+-0.10 / 90.00+-0.05 , the result is
0.06+-0.001

The Attempt at a Solution

the solution must either be
0.06 +- 0.00

or

0.06 +- 0.01x(10^(-1))

since the number of the significant numbers should be equal. so which one is it?

That "5.40+-0.10" is a little misleading. Although 5.40 is written as if it had 3 significant figures, that +-0.10 says that is is uncertain in the tenths place and so only has 2 significant figures. One way to do this is to calculate the largest possible value: 5.5/90.05= 0.6111 and smallest value: 5.3/89.95= 0.05886 That can be written as 0.06+-0.2.