Thank you for using the UCSC Genome Browser and for submitting your question regarding a fast way to find exon numbering based on a list of coordinates.
One way to view exon numbering is by using the UCSC Genome Browser graphical interface to view each coordinate, one at a time. Using your first coordinate as an example, navigate to the hg19 assembly Gateway Page, and then add the correct format of your coordinates by typing a colon directly after "chr1" like this: "chr1:43814978" and press the submit button.

You are now zoomed on chromosome 1 to a graphical representation of the single base pair of your coordinate. You can hover over the exon block of the gene MPL to see Exon (10/10). Please note that there are multiple transcripts for the gene MPL.
Here is a link to that position where you could alter the URL to arrive to your other positions:
http://genome.ucsc.edu/cgi-bin/hgTracks?db=hg19&position=chr1%3A43814978-43814978
(for example, swap in your chr3 178916853 information, the %3A represents a colon).
At the edge of each side in the viewer, you can also hover your mouse pointer over the directional arrows of each transcript to jump to the edges of the next and previous exons (you may wish to zoom out first).
From the UCSC Genes track, you can also click on any transcript's gene symbol name to find further exon information, such as the total number of exons (and the total number of coding exons) in any particular transcript.
If you have a long list of coordinates, please reply to this mailing list, and I can describe another way to output a list of exon numbers for each coordinate.
1.3. Table Browser Settings
Assembly: Feb. 2009 (GRCh37/hg19)
Group: Genes and Gene Predictions
Track: UCSC GenesTable: knownGene
Region: genome
Output format: custom track
Create one BED record per: Exons plus
chr3 178916537 178916965 uc003fjk.3_exon_1_0_chr3_178916538_f 0 +chr3 178917477 178917687 uc003fjk.3_exon_2_0_chr3_178917478_f 0 +
Step 2. Create a BED3 file of your coordinates. A BED3 file has 3 columns: 1) chromosome number, 2) starting position, and 3) ending position. Since you listed data points as an example, your coordinates will have the same starting and ending positions.
chr1 43814978chr1 43814980chr1 43815007chr3 178916853chr3 178916875
cat temp | awk '{print $1 " " $2 " " $2}'
chr1 43814978 43814978chr1 43814980 43814980chr1 43815007 43815007chr3 178916853 178916853chr3 178916875 178916875

Clade: Mammal
Genome: Human
Assembly: Feb. 2009 (GRCh37/hg19)
Track 1: "User_Track" Your subset (example data, N=5)Track 2: "tb_knownGene" Your superset of all exons, all genes, entire genome (hg19).


chr1 43814978 uc009vwr.3_exon_9_0_chr1_43814934_fchr1 43814978 uc001ciw.3_exon_9_0_chr1_43814934_fchr1 43814978 uc001civ.3_exon_9_0_chr1_43814934_fchr1 43814980 uc009vwr.3_exon_9_0_chr1_43814934_fchr1 43814980 uc001ciw.3_exon_9_0_chr1_43814934_fchr1 43814980 uc001civ.3_exon_9_0_chr1_43814934_fchr1 43815007 uc009vwr.3_exon_9_0_chr1_43814934_fchr1 43815007 uc001ciw.3_exon_9_0_chr1_43814934_fchr1 43815007 uc001civ.3_exon_9_0_chr1_43814934_fchr3 178916853 uc003fjk.3_exon_1_0_chr3_178916538_fchr3 178916875 uc003fjk.3_exon_1_0_chr3_178916538_f
chr1 43814978 uc009vwr.3_exon_9_0_chr1_43814934_f
chr1 43814978 uc009vwr.3_exon_10

Hi Cath,Thanks for your response.Yes, I do have a long list of targets(over 1000) for which I need to find exon number. If you can let me know a work around for this, it will be very helpful.RegardsHersh