Happy new year everyone!
It doesn't happen very often, but today I find myself in disagreement with Paul. The correct answer is (or should be) DECIMAL.
The "precision" mentioned on the BOL page about floating point data is not the number of decimal positions represented internally, but the number of decimal positions that can be trusted to be correct. The internal representation is different (base-2 to be exact). As mentioned on the top of the BOL page: "not all values in the data type range can be represented exactly". The value 0.1234567 is one of the many values that can not be represented exactly. When trying the code snippet in SSMS, this is carefully hidden - because SSMS knows about the number of "trustworthy" positions for the REAL data type and shows only that number of positions. Other front-end tools might not be so smart. And front-end or back-end applications that do further calculations on the number do get the internal representation, which in the case of the REAL data is not exactly correct.
Here is a modification of Paul's code that tricks SSMS into revealing a more accurate representation of the values internally stored; it shows that the DECIMAL value is indeed exact, but the REAL value is not.
[decimal] = CAST(@n1 * @n2 AS decimal(38,36)),
[real] = CAST(@n3 * @n4 AS decimal(38,36))
Hugo Kornelis, SQL Server/Data Platform MVP (2006-2016)
Visit my SQL Server blog: http://sqlblog.com/blogs/hugo_kornelis