# Decimal numbers lesson

## Decimal numbers facts

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

Example: 78.098

Integer part = 78

Fractional part = 098

3. Trailing zeros in the fractional part have no value so they are not necessary.

Example: 8.907000

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.

Examples:

0.7 - zero point seven

36.89 - thirty six point eight nine

## Place value of decimals

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.

Example: 123.45

## Relation between fraction and decimal

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.

Examples:

17 = 0....

13 = 0.333333333333...

9. If integer part of a decimal is > 0 then it can be represented as mixed fraction

Example: 1.5 = 1 12

10. Decimal fraction is a fraction whose denominator is a power of ten.

Examples:

810 = .8

8100 = .08