Decimals
Decimal number system is a positional notation with base 10. It is used to refer to numbers that have a fractional part separated from the integer part with decimal separator. Decimals help us to write fractional numbers without writing a fraction with numerator and denominator.
Decimal place value chart
In writing any number, the position of each digit is very crucial.
Thousands 
Hundreds  Tens 
Ones 
Decimal point

Tenths 
Hundredths 
Thousandths  Ten thousandths 
When we move to the right in the above place value chart, the value of digit becomes ten times smaller i.e. one tenth and when we move to the left in the chart, the value of digit becomes ten times bigger.
Onetenth
We can write it as .
Onetenth
One part of equal parts is onetenth and written as or .
One – hundredth
We can write it as
Onehundredth
One part of equal parts is one – hundredth and written as or .
One–thousandth
We can write it as 0.001.
Reading and Writing Decimal Fractions
Every decimal number has two parts, a whole/integral part and a decimal part. A dot (.) called decimal point separates the integral and decimal part.
Example.
is a decimal fraction and can be represented as
Placing the above decimal fraction in decimal place value chart.
Thousands 
Hundreds 
Tens 
Ones 
Decimal point 
Tenths 
Hundredths 
Thousandths 
The above number read as Forty three point six seven eight or Forty three and six hundred seventy eight thousandth.
Expanded Form of Decimals
By writing decimal in its expanded form, we can show value of each digit.
Writing Decimals in Expanded Form
Step1: Place the number in decimal place value chart.
Step2: Now, write the value of each digit of decimal fraction.
Example 1.
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart
Thousands 
Hundreds 
Tens 
Ones 
Decimal Point 
Tenths 
Hundredths 
Thousandths 
Ten thousandths 
6  7 
Step2: Now, write the value of each digit of decimal fraction.
tenths hundredths.
OR
Example 2.
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart
Thousands 
Hundreds 
Tens 
Ones 
Decimal Point 
Tenths 
Hundredths 
Thousandths 
Ten thousandths 
5  0  7 
Step2: Now, write the value of each digit of decimal fraction.
tenths hundredths
OR
Example 3.
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart
Thousands 
Hundreds 
Tens 
Ones 
Decimal Point 
Tenths 
Hundredths 
Thousandths 
Ten thousandths 
4  7  8  8  3  1 
Step2: Now, write the value of each digit of decimal fraction.
hundred tens ones hundredths thousandths
OR