Assuming a simple random sample or a simple systematic sample from a large population the sample size required to estimate a proportion with a 95% CI of a give width:
n = (p * (1 - p)) / (e / 1.96)^2
where p is the proportion being estimated (0.45 in your case) and e is the require half-width of the 95% CI. If we table p = 0.45 (45%) and e = +/- 0.05 (5%) then:
n = (p * (1 - p)) / (e / 1.96)^2
n = (0.45 * (1 - 0.45)) / (0.05 / 1.96)^2
n = 380
Most practical samples that we use will have two or more stages. Anything that differs from a simple ramdom sample will have a design effect. I wonder what you mean by an "entire district" sample. Such a sample is the aim of cluster surveys like SMART. An "entire district" sample might use a spatially stratified sample. This will tend to give low design effects and it may be OK to ignore design effects. A smart type survey may have large design effects. Design effects can be small if you have many small clusters and prevalence that is pretty constant wherever you go then design effects will likely not be very large.
Unless you have a simple ramdom sample then I think you should (1) specify a design effect and (2) analyse the data in a way that takes into account the sample design. For the design effect, a safe design effect would be 1.5 or 2.0 (SMART people can advise). for a design effect of 1.t we have:
n = DEFF * ((p * (1 - p)) / (e / 1.96)^2)
n = 1.5 * ((0.45 * (1 - 0.45)) / (0.05 / 1.96)^2)
n = 570
ENA for SMART can analyse data from a simple random sample and from a two stage PPS cluster sample. For other designs you can use SUDAAN, STATA, R, SPSS, EpiInfo, &c.
I hope this is of some use.