The system of fractions expressed by the use of the decimal point, that is, fractions in which the denominator is any higher power of 10. Thus 3/10, 51/100, 23/1,000 are decimal fractions and are normally expressed as 0.3, 0.51, 0.023. The use of decimals greatly simplifies addition and multiplication of fractions, though not all fractions can be expressed exactly as decimal fractions. The regular use of the decimal point appears to have been introduced about 1585, but the occasional use of decimal fractions can be traced back as far as the 12th century.