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, Decimal = 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.
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23--or, in decimal fractions of a day, as astronomers like to time things, on Feb.
As students become familiar with the activity demonstrating multiple groupings of the whole, half and quarter, this can be extended to the understanding of discrete models for fractions and later further developed to show the relationship between standard fractions, decimal fractions and percentages.
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Bruce Moody has contributed an article explaining how he uses a maths manipulative called "decipipes" to challenge students' conceptions or misconceptions about decimal fractions.
Conceptual bases of arithmetic errors: The case of decimal fractions.
Danika's responses illustrate the difficulty that some students have in transferring their knowledge of decimal fractions to number lines.
The building materials are conceptual understanding and the ability to perform arithmetic manipulation on whole numbers, decimal fractions, and common fractions.
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.
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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).
Rosemaree Caswell, in her article Developing decimal sense, describes a sequence of activities she has found successful in helping middle years students develop a deeper understanding of decimal fractions and therefore assist with this transfer of understanding to real-life situations.