When is it necessary to include the GST/HST No on the Home Accessibility Expense worksheet? The column header states "if applicable."

[KateQuinn]

If the business charges you tax, they should have a GST/HST number to verify they are registered for GST/HST. 
If the is not registered for GST/HST, then you would not need to include a GST/HST number (because they would not have one) and they should not be charging you tax.

You can confirm the number by checking the GST/HST Registry. When entering the GST/HST number, enter the first 9 digits (no letters). 

"A supplier must include the GST/HST account number on receipts, invoices, contracts, or other business papers it gives out when it supplies taxable goods or services of $30 or more.

If you can't find the GST/HST account number, contact your supplier. When your supplier does not provide their GST/HST account number, call the Canada Revenue Agency's Business enquiries line at 1-800-959-5525 to confirm it is registered."

As per the Canada Revenue Agency (CRA): Confirming a GST/HST account number - Canada.ca

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