Introduction
Expanded form is the method of pulling a number apart and expressing it as a sum of the values of each digit.
Best way to identify the expanded form of a number is to simply write the number in words. Place value by adding means representing the value in expanded form. Depending on the digit the place value is added.
Note: If they are 3 digits then
1st value is hundred place
2nd value in tens place
3rd value in ones place
Example:
Represent 234 in place value form
Here they are 3 digits
2is in hundred place last or right digit is the ones' place
3 is in tens place
4 in tens place
Expanded Form of Numbers
The numbers can be expanded based on digits (Hundred+thousands+tens=3digits)
Two digit expanded form:
11= 10+1
22= 20+2
33= 30+3
44= 40+4
54=50+4
64=60+4
74=70+4
85=80+5
99=90+9
Three Digit Expanded Form
172=100+70+2
156=100+50+6
239=200+30+9
345=300+40+5
456=400+50+6
576=500+70+6
678=600+70+8
734=700+30+4
876=800+70+6
978=900+70+8
988=900+80+8
Similarly we can write for all numbers depending on number of digits.
Place Value
In order to understand the concept of expanded form need to understand about place value.
Place value
Place value is a positional system of notation in which the position of a number with respect to a number of digits to determine the value of the digit.
Example:
Represent 564 in place value form
Here they are 3 digits
5 is in hundred place
6 is in tenths place
4 is in first place
Properties
1) Place value helps in identifying the digits place in given number
2) Representation of number to word form will be easy
3) Can easily solve problems of picture to donate in digits form and giving place value.
Place value can be obtained from:
1) Place value of decimal form
2) Place value by adding
3) Place value from words
Types of Expanded Form
1. Expanded form of whole numbers
2. Expanded form of decimal numbers
Expanded form of whole numbers
Here whole numbers are added based on the place value concept that’s number of digits for whole numbers.
Place value can be identified by number of digits; these values which are identified can be expanded and represented in word form and many other ways.
Digits can be represented based on the number:
Suppose if they are 4 digits then
1st digit start with thousand
2nd digit-hundreds
3rd digit-tens
4th digit –ones
Example:
Represent the given digit in word form 456?
Given digit:Number of digit-3
So the place value starts with hundred, tens and ones.
4 is in hundred place
5 is in tens place
6 is in ones place
The given digit is “four hundred and fifty six “
Expanded Form of Decimal Numbers
Decimal is a number that is written with a decimal point in it. The value of the digits is based on the number ten. The decimal numeration system is based on base 10.
Note: In decimal the place value depends on the base system.
Example: In the decimal (base ten) system, the value of the digits is based on the number ten.
Properties
1) Each position in a decimal number has a value that is a power of 10.
2) A decimal point separates the non-negative powers of 10
3) Positive exponents on left and negative exponents on right.
In expanded form of decimals first we need to follow the above steps:
1. First we need to check the decimal position
2. Before decimals we need to count the digits, depending on that we will represent in the word form.
3. Then the point after decimal is considered as tenth, hundredth so on…