1. What is decimal numbers?
Like fractions, decimal numbers represents numbers between two numbers or decimals.
Each fraction can be represented as a decimal and each decimal can be represented as a fraction.
2. Decimal number has two components and they are separated by a . (dot) which is called a decimal point
Integer part - left of decimal point
Fractional part - right of decimal point
Integer part = 78
Fractional part = 098
3. Trailing zeros in the fractional part have no value so they are not necessary.
3 zeros after .907 has no values. 8.907 can be represented as 8.907
4. How to read a decimal
The integer part is read similar to the whole numbers.
Decimal places (Fractional parts) are read as individual numbers from the decimal point towards the right.
0.7 - zero point seven
36.89 - thirty six point eight nine
5. Value of a digit increases 10 time when moving towards left of decimal point. when moving right of decimal point values decreased to one-tenth.
6. Fractions can be converted into decimal. Some fractions results in infinite number of decimals.
7. If a fraction with denominator whose only prime factors are 2s & 5s then those numbers have limited decimal numbers.
8. If a fraction with denominator has any prime factors other than 2 or 5 then it cannot be expressed as a finite decimal fraction. It has a unique eventually repeating infinite decimal.
1⁄7 = 0....
1⁄3 = 0.333333333333...
9. If integer part of a decimal is > 0 then it can be represented as mixed fraction
Example: 1.5 = 1 1⁄2
10. Decimal fraction is a fraction whose denominator is a power of ten.
8⁄10 = .8
8⁄100 = .08