The decimal number is a form of record of fractional number. The whole part of such number separates from fractional a divider — a point or a comma. The decimal form of record is applied to conducting accounting of money at cash and non-cash flow, on displays of computing devices and office equipments.
Instruction
1. Record of number in a decimal form looks as a number of figures from a dividing comma (or a point) between them. To the left of a divider the whole part of number, on the right — fractional is located. Figures of a fractional part are called decimal signs. The decimal number can be final, infinite periodic and infinite acyclic.
2. In the form of final decimal fraction it is possible to write down number in case a fractional part of number expresses quantity of shares whole, multiple to ten. Therefore, in the form of final decimal number the simple fraction with a denominator, multiple to ten can be written down: 10, 100, 1000, etc. Decimal record of simple fraction with a denominator, multiple to ten, looks so: zero, dividing comma, numerator of simple fraction. At decimal record of the mixed number the comma is faced by the whole part of number. For example, the simple fraction 7/10 in a decimal form looks so: 0.7. The mixed number 17 ⁴/₁₀₀ in a decimal form registers so: 17.04.
3. Simple fractions with a denominator 2 or 5 are easily given to a denominator 10 and can be written down in the form of final decimal fraction. For example, the fraction 3/5 is given to a denominator 10 by multiplication of numerator and a denominator by two: 3/5 = 6/10. The decimal form of record of such number looks so: 0.6. The fraction ½ multiplication of numerator and a denominator on five turns into 5/10 and in decimal notation looks so: 0.5.
4. To transfer to a decimal form the number is less than unit, written down in the form of simple fraction with the denominator not equal 2, 5, 10 and not multiple to ten, it is necessary to divide numerator of simple fraction into its denominator. Further to write down decimal number in a format: zero, dividing comma, result of division of numerator of simple fraction into a denominator.
5. If division of numerator of simple fraction into its denominator came to the end without the rest, then this simple fraction can be written down in the form of final decimal fraction. For example, the simple fraction 11/16 in decimal notation looks so: 0.6875.
6. If at division of numerator into a denominator a certain sequence of figures as a result begins to repeat, then it means that the period of infinite periodic decimal number was created. The group of figures forming the period at record of number is not repeated, and written down once and bracketed. For example, the simple fraction 7/11 in a decimal form can be written down so: 0,(63).
7. If at division of numerator into a denominator the period is not formed, it means, something it consists of very large number of figures, or the number has no period at all. Then the number of decimal signs at record of number is dictated by requirements to the accuracy of calculations.