You could calculate the confidence intervals for the SIR (O/E) and since your measure as a fraction is (O -E)/O  = 1 -E/O  = 1-1/SIR, just calculate its range for the two extremes of SIR substituted in the equation. Approximate and exact methods for confidence intervals for SIR or SMR are given in attached extract from Breslow and Day Vol ii 1987 IARC.

you can write the expression as

SIR = (1–obs/exp)*100 = 100 – obs*100/exp

where "exp" is a constant and obs is the only random variable.

Is the number of observed cases large enough to justify a good approximation of the sampling distribution of the observed values to the normal distribution? If this sampling distribution of obs is assumed to be (approximately) N(µ, σ²), then obs*a is distributed as N(µ*a, σ²*a²), so obs*100/exp is distributed as N(µ*100/exp, σ²*(100/exp)²), and SIR is distributed as N(100 – µ*100/exp, σ²*(100/exp)²).

Hence, if µ and σ² give the mean and the variance of the Gaussian sampling distribution of "obs", then you can calculate the confidence limits for SIR from the normal distribution with mean 100 – µ*100/exp and variance σ²*(100/exp)².

You could calculate the confidence intervals for the SIR (O/E) and since your measure as a fraction is (O -E)/O  = 1 -E/O  = 1-1/SIR, just calculate its range for the two extremes of SIR substituted in the equation. Approximate and exact methods for confidence intervals for SIR or SMR are given in attached extract from Breslow and Day Vol ii 1987 IARC.

What is usually calculated is (Obs/ Expected) * 100 which is also known as a Standardized Mortality Rate. What you quote is a chi-square like test of whether  the rate is elevated or lower than expected. This is sometimes used in a 'signed' form by taking account of whether the observed is above or below the expected.

https://www.researchgate.net/publication/11114068_The_use_of_Chi-square_maps_in_the_analysis_of_census_data

So you could compare your value ( in its un-signed form)  with the chi-square statistic with 1 degree of freedom. 

But for small counts this is problematic ( remember the rule of thumb of the  expected being greater than 5 for a chi-square test). Consequently people often used a test based on the Poisson distribution as it can deal with rare counts

See 

 SIMPLE METHOD TO CALCULATE THE CONFIDENCE INTERVAL OF A STANDARDIZED MORTALITY RATIO (SMR) http://aje.oxfordjournals.org/content/131/2/373

If you have lots of these to estimate you should then be concerned about multiple testing ( the Texas sharp-shooter problem) ;

https://en.wikipedia.org/wiki/Texas_sharpshooter_fallacy

If that is the case you may want to have a look at the modelling approach of this paper which shrinks the unreliable rates according to their uncertainty and models all the rates simultaneously in an overall random effects Poisson model

https://www.researchgate.net/publication/266383638_A_model-_based_approach_to_the_analysis_of_a_large_table_of_counts_occupational_class_patterns_in_among_Australians_by_ancestry_generation_and_age_group

You may also be interested in my (long!) answer to this question

https://www.researchgate.net/post/Are_p-values_and_significance_tests_still_meaningful_in_census_data_analysis

Article The use of Chi-square maps in the analysis of census data

Article A model- based approach to the analysis of a large table of ...