The Canada Revenue Agency describes in detail here what information businesses must generally include on their invoices so that GST/HST registrants can claim Input Tax Credits (ITCs) for the expenses. Quote:
Sales invoices for GST/HST registrants
You have to give customers who are GST/HST registrants specific
information on the invoices, receipts, contracts, or other business
papers that you use when you provide taxable goods and services. This
information lets them support their claims for input tax credits
(ITCs) or rebates for the GST/HST you charged. [...]
The page quoted continues with a table describing what, specifically, needs to be on a sales invoice based on the total amount of the invoice; the requirements differ for: total sale under $30, total sale between $30 to $149.99, and total sale $150 or more.
For the total sale under $30 category, the only things a sales invoice must contain to support an ITC claim are (1) the provider's business name, (2) the invoice date, and (3) the total amount paid/payable. i.e. When the total sale is under $30, there is no requirement for any GST/HST amount to be indicated separately, nor for a business number to be present on the invoice.
Hence, IMHO (and I am neither an accountant nor a lawyer), if your Uber rides are for $30 or less, then you shouldn't expect a GST/HST number anyway, and a simple invoice as described should be enough for you to claim your ITCs. Whether or not the provider is registered in fact for GST/HST is beside the point.
For amounts over $30, you need a bit more. While the page above specifies that the provider's business number should be included beginning with the next level of total sales, there are exceptions to those rules described at another page mentioned, Exceptions to invoice requirements, that specifically apply to the taxi/limousine case. Quote:
Exceptions to invoice requirements
GST/HST registrants are required to keep the necessary documentation
to support their claim for ITCs and rebates. In certain circumstances
the documentation requirements have been reduced.
For taxi or limousine fares your books and records must show:
- the supplier's name or trade name;
- the date of the supply;
- the fare; and
- the amount of GST/HST charged, or a statement that the fare includes GST/HST. [emphasis mine]
So at a minimum, for fare in excess of $30 total, you should ask the driver to note either (a) the amount of GST/HST charged, or (b) a statement that the fare includes GST/HST. The driver's business number need not be specified. Consequently, if your receipt for a ride in excess of $30 does not contain any such additional information with respect to GST/HST, then I would expect the receipt does not satisfy the CRA's requirements for supporting your ITC claim.
i.e. Keep your individual rides under $30 each, or else get a better receipt from the driver when it is above that amount.
p.s. It should go without saying, but your rides, of course, must be considered reasonable business expenses in order to qualify for GST/HST ITCs for your business. Receipts for rides of a personal nature are not eligible, so be sure to maintain proper records as to the business purpose and destination for each ride receipt so claimed.