Decimals in Expanded Form

 

Generally fractions are in the form `(a)/(b)` . Here ‘a’ is known as numerator and ‘b’ is the denominator. Here we can use some special fractions that having the denominator powers of 10. That us the denominators are 10, 100, 1000 etc. These special fractions are known as decimal fractions. Let us use these fractions is represented in a new way. That is

 

`(1)/(10)`  can be pronounced as ‘one-tenth’ and is written  decimal fraction as ‘0.1.`(1)/(100)` can be pronounced as ‘one-hundredth’ and is written decimal fraction as ‘0.01.`(1)/(1000)` can be pronounced as ‘one-thousandth’ and is written decimal fraction as ‘0.001.


Expressing the Decimal Numbers in Place Value Form


Our number system is developed with ten as the base. The place value of the given number increases in powers of ten from the direction right to left and decreases in powers of 10 from the direction left to right. Let us learn about the place value of digits in decimal numbers. If the denominator of a fractional number is not10 or its powers, then it can be expressed in the form whose denominator is raised to 10 or a power of 10.Examples of Decimals in Expanded Form


Ex 1:Express decimal 2843.654 in the place value table and in expanded form.
This number is pounced as, Two thousand eight hundred forty three point six five four.


We can write this number in expanded form as:


chart


2843.654 = (2 × 1000) +( 8 × 100) + (4 × 10) + (3 × 1) + (6 x `(1)/(10)` ) + (5 x `(1)/(100)` ) + (4 x `(1)/(1000)` )
This is the decimal expanded form.


Ex 2: Express the decimal in expanded form 8.37
Solution: 8.37 = (8 × 1) +( 3 × `(1)/(10)` ) + (7 x `(1)/(100)` )

 


This is the decimal expanded form.


Ex 3:Express the decimal in expanded form 15354.89
Solution: 15354.89 = (1 x 10000) + ( 5 x 1000) + ( 3 x 100) + ( 5 x 100) + ( 4 x 10) +(8 x `(1)/(10)` x `(1)/(100)`


This is the decimal expanded form.