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I would use compatible numbers to estimate the quotient for 1089 divided by 99 by estimating the numbers first. Then I would use compatible numbers. After I would cancel the zero's,divide, and after put in zero's because if you divide the estimated quotients you will get a whole number. It would be easier to divide compatible number's if the estimated number's will give you number's that divide evenly. If you pick estimates that are close to the number you will get pretty close to your real answer.
The best way to estimate a quotient using compatible numbers is to first understand how compatible numbers work. They are numbers that are close in value to the actual numbers and are easily added, subtracted or divided.
8.6932
6.9877
19.8889
3.8667