Addition - Adding Decimal Fractions

Together, the rational and irrational numbers constitute the set of real numbers. Addition of real numbers is facilitated by extending the positional notation used for integers to decimal fractions. Place a period (called a decimal point) to the right of the ones column, and let each column to its right contain numbers that are successively smaller by a factor of ten. Thus, columns to the right of the decimal point represent numbers less than one, in particular, "tenths," "hundredths," "thousandths," and so on. Addition of real numbers, then, continues to be defined in terms of counting and carrying, in the manner described above.