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.
References in periodicals archive ?
It was very disappointing to see that there was only a small change in understanding of decimal notation during the course of a complete school year.
The first algorithm involves a clever use of decimal notation to rewrite numbers in non-standard form so that in each place numbers of sufficient magnitude exist to carry out the subtractions without use of negative numbers (for example, as in rewriting 36 to 20 + 16 before subtracting 9 in the ones column).
After further investigation, it was interesting to find that other teachers and researchers had also identified this misconception and suggested that it was related to the "symmetry" of the decimal notation (Ball & Bass, 2000; Chinn, 2008; Hiebert, Wearne & Taber, 1991; Ministry of Education, Ontario, 2006; Moskal & Magone, 2000; Resnick, Nesher, Leonard, Magone, Omanson & Peled, 1989).
Students had great difficulty relating the decimal notation to the picture.
The recording table provides evidence of the student's capacity to move appropriately between fraction notation and decimal notation, to match these to an appropriate amount of shaded area on the model, as well as facility with the addition of decimals.
Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation.
But time spent on developing students' understanding of the decimal notation is not time wasted.
As with the situation in Germany, our students are also familiar with using decimals in real life with decimal notation found in everything from money to petrol prices, displayed prominently in a variety of forms and discussed frequently in conversation both at home and at school.
Next, ask the students to shade one-eighth of the grid and to determine a name for 1/8 using decimal notation.
to explore fractions in both common fraction and decimal notation.
Results from a large scale study of students' misconceptions of decimal notation (Steinle & Stacey, 2004) indicate many students treat decimals as another whole number to the right of the decimal point.