Decimal numbers that may be expressed as a fraction, the denominator of which is a power of ten. For example, the numerals formula_5 represent the fractions , , . More generally, a decimal with digits after the separator represents the fraction with denominator , whose numerator is the integer obtained by removing the separator. Expressed as a fully reduced fraction, the decimal numbers are those, whose denominator is a product of a power of 2 by a power of 5. Thus the smallest denominators of decimal numbers are The "integer part", or "integral part" of a decimal is the integer written
Decimal floating point The following example is decimal, which simply means the base is 10. This is nothing other than converting to scientific notation. In detail: This is the true result, the exact sum of the operands. It will be rounded to 7 digits and then normalized if necessary. The final result is: Note that the low 3 digits of the second operand (654) are essentially lost. This is round-off error. In extreme cases, the sum of two non-zero numbers may be equal to one of them: Another problem of loss of significance occurs when two close numbers are subtracted. e=5; s=1.234571 and