Decimal Number
Definition and Basic Features
The Decimal Number System is a base-10 system represented by digits from 0 to 9 (0,1,2,3,4,5,6,7,8,9). This system, which we use in daily life, is also known as the Hindu-Arabic numeral system.
Example: 7310 , 13210 , 526710 → The subscript indicates the base.
Structure of Decimal Numbers
1. Whole Part and Decimal Part
- Whole Part: The part to the left of the decimal point (Example: 15. 75 → 15).
- Decimal Part: The part to the right of the decimal point (Example: 15. 75 → 75).
2. Place Values
| Units | Tenths | Hundredths | Thousandths |
|---|---|---|---|
| 1 | 0.1 | 0.01 | 0.001 |
Decimal Numbers and Fractions
1. Converting Fractions to Decimal Numbers
- Steps:
- Divide the numerator by the denominator.
- Place the decimal point accordingly.
2. Converting Decimal Numbers to Fractions
- Steps:
- Count the decimal places and use a power of 10 as the denominator.
- Form the numerator by including the whole number.
Examples of Conversions
1. Fraction → Decimal Number
2. Decimal Number → Fraction
Addition and Subtraction with Decimal Numbers
When adding or subtracting decimal numbers, the decimal points must be aligned. If there are missing digits, zeros are added to the right.
Example: Addition
- 2.34 + 1.56
Example: Subtraction
- 5.67 – 2.34
Multiplication with Decimal Numbers
When multiplying decimal numbers, multiply the numbers as if there were no decimal points. Then, count the total number of decimal places in the numbers being multiplied and place the decimal point in the result accordingly.
Example: Multiplication
- 1.2 × 0.3
Division with Decimal Numbers
When dividing decimal numbers, adjust the divisor and dividend by multiplying both by powers of 10 to eliminate the decimal points. Then, perform the division as usual.
Example: Division
- 4.5 ÷ 0.5
Comparing Decimal Numbers
When comparing decimal numbers, first compare the whole number parts. If the whole parts are equal, compare the decimal places one by one.
Example: Comparison
- Arrange 3.14, 3.2, and 3.09 in ascending order:
