Decimals
Reading and Writing Decimals
 Fraction is used to express a part of a whole thing.
 A decimal is another representation of a fraction where a whole number part and the fractional part are written together.
 A whole number and the fractional part are separated by the dot known as a decimal point, â€ś.â€ť.
Understanding decimals from fraction
 A fraction where the denominator (lower part) is in the power of 10, i.e., 10, 100, 1000, etc. is called a decimal fraction.
 A decimal fraction can be written using the decimal point (that is without the denominator).

We know that the fraction 5/The denominator of the fraction
5 / 10has 1 zero. Therefore, in decimal representation, after a decimal point, there will be one digit.10 means â€ś5 out of 10 partsâ€ť.
 In decimal fraction it can be written as 0.5.
Example:
Place Value
 The place value of the digit is the actual position value of the digit.
 The place value of the decimals is found using the place value chart.
 The number to the left of the decimal point represents the whole number.
 The number to the right of the decimal point represents the fractional part.
 As we go to the left of the decimal chart the place value of the number is 10 times greater than the previous place value.
Example:
Find the place value of every digit in the number 23.46.
Solution:
 The number 2 is in the tens place. Therefore, the place value of 2 is 2 Ă— 10 = 20.
 The number 3 is in the one place. Therefore, the place value of 3 is 3 Ă— 1 = 3.

The number 4 is in tenth place. Therefore, the place value of 4 is
4 / 10or 0.4.

The number 6 is in the hundredth place. Therefore, the place value of 6 is
6 / 100or 0.06.
Expanded Form
An expanded form of the decimal is the sum of the place value of each digit in the number.
Example 1:
Expand the number 345.167
Solution:
The expanded form of 345.167 is:
300 + 40 + 5 +Example 2:
Write in decimal notation 500 + 30 + 2 +Solution:
The decimal representation is 532.256.
Equivalent Decimals
 Two decimals are said to be equivalent decimal if it has the same value.
 The decimals 0.6 and 0.60 are equivalent decimals as it has the same value.
 By adding zeros on the right of the decimal numbers we get an equivalent decimal.
Reading Decimals
Steps to write the decimals in words:
 Start reading the numbers from the left of the decimal place as a whole number.
 Read point for the decimal point.
 Read the digits to the right of the decimal point as a single whole number.
Example :
Decimals in figure  Decimals in words 

0.216  Zero point two one six 
61.724  Sixtyone point seven two four 
123.6542  One hundred twentythree point six five four two 
Alternate way
The alternate way of naming the decimals is with the use of the decimals place value chart.
 Read the number to the left of the decimals point as a whole number.
 Read and for the decimal point.
 Observe the position of the last digit and name accordingly.
Decimals in figure  Decimals in words 

0.216  Two hundred and sixteen thousandths. 
61.72  Sixtyone and seven two hundredths. 
123.6  One hundred twentythree and six tenths. 