# decimal

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## decimal

1. a fraction that has a denominator of a power of ten, the power depending on or deciding the decimal place. It is indicated by a decimal point to the left of the numerator, the denominator being omitted. Zeros are inserted between the point and the numerator, if necessary, to obtain the correct decimal place
2. any number used in the decimal system
3.
a. relating to or using powers of ten
b. of the base ten
4. expressed as a decimal

## Decimal

a fraction whose denominator is a whole power of the number 10. The decimal is written without a denominator, setting off in the numerator to the right of the decimal point as many digits as there are zeros in the denominator (for example, 485,634/1,000 = 485.634 and 3/100 = 0.03). In such notation, the part to the left of the decimal point designates the integer part of the fraction. The first digit after the decimal point designates the number of tenths; the second, the number of hundredths; and so forth.

The decimal notation of rational numbers whose denominator does not have other prime factors except 2 and 5 contains a finite number of digits (for example, 4/25 = 0.16). In general, the digits in the decimal notation of a rational number begin repeating at some position; such a number is an infinite repeating decimal (for example, 7/6 = 1.1666 …). Irrational numbers are nonrepeating infinite decimals (for example, = 1.41421 . … In all cases, the decimal of akak-1a0b1b2 … can be written in the form

where ak, ak-1, … , a0, b1b2, are the numerals 0, 1, 2, … , 9 (ak ≠ 0) in the corresponding digit of the number. For example, 382.1274 = 3 x 102 + 8 × 10 + 2 + 1/10 + 2/102 + 7/103 + 4/104, that is, here a2 = 3, a1 = 8,a0 = 2, b1 = 1, b2 = 2, b3 = 7, and b4 = 4. Decimals were already used in the 14th-15th centuries. The Samarkand mathematician Al Kashi described the decimal system in 1427. In Europe, the decimal was introduced by S. Stevin in 1584.

## decimal

[′des·məl]
(mathematics)
A number expressed in the scale of tens.

## decimal

Meaning 10. The numbering system used by humans, which is based on 10 digits. In contrast, computers use binary numbers because it is easier to design electronic systems that can maintain two states rather than 10.
References in periodicals archive ?
Decimal fractions differ from common fractions because they have 10 or a power of 10 for a denominator, whereas common fractions can have any number for the denominator.
The theoretical rate was based on the percentages, converted to decimal fractions, provided by Fehr (1987).
She said that she was confident of her procedural knowledge, but was unsure of some of the different ways of conceptualizing and relating common and decimal fractions.
Once the students have mastered body fractions using standard fractions and set values, the activity can be extended to percentages and decimal fractions.
It showed that the content areas like natural numbers, common fractions, and decimal fractions were given the highest weight 171/2 % each (i.
Some of the mathematics topics addressed are factors, measurement, fractions, decimal fractions, and multiplication.
Danika's responses illustrate the difficulty that some students have in transferring their knowledge of decimal fractions to number lines.
This could lead them to conjecture that decimal fractions will terminate if their denominator is any combination of powers of 2 and powers of 5.
The results reported in the article are not at all surprising when you read (1) that money is clearly the favored context used to teach decimals, and (2) that common and decimal fractions are treated as separate entities.
The reader may also be interested in the Decimat game (Roche, 2010), which uses a similar model and game to assist students' developing understanding of decimal fractions.
Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions.
A considerable body of research exists on students' understanding of decimal fractions and the prevalence and persistence of common misconceptions related to this understanding (Steinle & Stacey, 2004).

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