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2/3 = .66 It is a repeating decimal.
When you multiply decimals, the decimal point is placed in the product.
If the two decimal numbers have x and y digits after the decimal points, then the product has (x + y) digits after the decimal point.
Because terminating or repeating decimals can be written as the quotient of two integers a/b, where b is not equal to zero.
All rational fractions - one integer divided by a non-zero integer - give rise to repeating or terminating decimals. If, for the fraction in its simplest form, the denominator can be expressed as a product of powers of only 2 and 5 then the decimal will terminate. If the denominator has any prime factor other than 2 or 5 the decimal will be recurring. All non-rational fractions will have infinite, non-recurring decimal representations.