How Correctly to Prorate Rent on a Lease Renewal

[Alan Roebuck]

One of our single-family-home tenants is renewing her lease. The new lease will take effect on October 23, and the new rent is higher. So her total rent payments for October will be 22 days under the old rent and 9 days under the new rent.

My question: Is there a legal requirement to prorate by assuming a 30-day month?  Since October actually has 31 days, calculating the per-day rent by dividing by 30 actually increases the total rent the tenant would have to pay. Calculating the more accurate rent by dividing the monthly rent by 31 actually gives the tenant less rent to pay, but I want to do it legally.  And if it makes a difference, the property is in California.

Any insight would be appreciated.