Decimal Fractions
Decimal fractions are a form of representation of rational numbers. They allow the expression of quantities that are not whole numbers, but fall between two whole numbers. Decimal fractions are essential in many fields, such as mathematics, science, finance, etc. They enable precise calculations and the representation of intermediate values with great accuracy.
Definition of Decimal Fractions
Definition
Decimal Fraction
A decimal fraction is a fraction whose denominator is a power of 10. It can be written in decimal form, that is, with a point followed by a series of digits.
Example
For example, the decimal fraction 0.75 can be read as "seventy-five hundredths." It represents the number that is equivalent to dividing 75 by 100, which is 0.75.
Conversion between Decimal Fraction and Whole Number
It is often useful to convert a decimal fraction to a whole number, or vice versa. To do this, simply apply the basic conversion rules.
To convert a decimal fraction to a whole number, you simply multiply the fraction by the appropriate power of 10. For example:
- 0.75 * 100 = 75
- 0.125 * 1000 = 125
- 0.9 * 10 = 9
To convert a whole number to a decimal fraction, you simply divide the number by the appropriate power of 10. For example:
- 75 / 100 = 0.75
- 125 / 1000 = 0.125
- 9 / 10 = 0.9
Operations with Decimal Fractions
Fundamental operations such as addition, subtraction, multiplication, and division can be carried out with decimal fractions in the same way as with whole numbers. You just need to treat them like ordinary decimal numbers and apply the appropriate rules.
Summary
Key Points:
Decimal fractions are essential tools for accurately representing intermediate quantities. They can be converted to whole numbers and vice versa by applying the appropriate conversion rules. Basic mathematical operations can also be performed with decimal fractions. It is important to master these concepts to effectively manipulate decimal numbers.