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If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
The lattice technique can also be used to multiply decimal fractions. For example, to multiply 5.8 by 2.13, the process is the same as to multiply 58 by 213 as described in the preceding section. To find the position of the decimal point in the final answer, one can draw a vertical line from the decimal point in 5.8, and a horizontal line from ...
Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.
A number has a terminating or repeating expansion if and only if it is rational; this does not depend on the base. A number that terminates in one base may repeat in another (thus 0.3 10 = 0.0100110011001... 2). An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases.
During the primary school years, children learn about whole numbers and arithmetic, including addition, subtraction, multiplication, and division. [27] Comparisons and measurement are taught, in both numeric and pictorial form, as well as fractions and proportionality, patterns, and various topics related to geometry. [28]
Multiplication is often defined for natural numbers, then extended to whole numbers, fractions, and irrational numbers. However, abstract algebra has a more general definition of multiplication as a binary operation on some objects that may or may not be numbers. Notably, one can multiply complex numbers, vectors, matrices, and quaternions.