Expanded form refers to a way of writing numbers so as to see the math value of individual digits. It certainly requires some skill to write the numbers in expanded form. Students can explore more about expanded form and how to write numbers in it here.
What is Expanded Form?
Expanded form refers to a way of writing numerical values such that it breaks up the value into separate digits. This shows how much each digit represents in the process.
In expanded form, the breaking up of a number takes place according to their place value. Then expansion must take place so as to show the value of each digit.
In expanded form, separation of numbers takes place into individual place values and decimal places. Consequently, they can form a mathematical expression.
Understanding of the Place Values
An individual must try to count from zero: 0,1,2,3,4,5,6,7,8. This counting is quite straightforward. However, when the individual reaches 10, something certainly changes.
Now the individual has to deal with two digits in the number. Furthermore, each digit occupies a slot in the final number. Also, each place has a different value.
The slot on the left indicates tens. Moreover, the digit 1 in that slot indicates that an individual has one 10. Furthermore, the slot on the right indicates ones.
Ones are the same numbers the individual began counting with. Finally, zero in the slot tells that the individual does not have any extra 1s.
Examples of Place Values
If an individual; keeps counting, he would notice something. The individual would notice that the digits in the ones column are the first to change. The next number is certainly 11.
Decomposing the number means taking it apart to its component place values. During decomposing the number, the individual would notice that there is a 1 in the tens slot.
Furthermore, the individual would notice that there is a 1 in the ones slot. Therefore, the individual would have one 10 and one 1.
The next number one must deal with is 12. 12 certainly has a 1 in the tens slot. However, there is a 2 in the ones slot. If the individual keeps counting long enough, then he would eventually reach 19, then 20.
One must notice that the number in the tens slot has been increased to 2. However, the one’s slot has been reset to zero. This pattern continues as the individual counts up.
The number is the slot of ones keeps on increasing until 9 is hit. Afterwards, the value of tens goes up. Also, the value of the ones is reset to zero.
Writing Numbers in Expanded Form
Expanded form is a unique way of writing digits of a number which has been broken into each of its component place values.
In order to write numbers in expanded form, an individual must link each digit in the number to its place value. This must take place with a multiplication sign.
One can take the example of 392. Reading from the left to right, one would start with the biggest slot, the hundreds place. This slot has a 3 in it.
The individual would have 3 × 100 = 300. The next slot on the right is certainly the tens place. Furthermore, there is a 9 in it. So, one would have 9 × 10 = 90.
Finally, there is a 2 in the one’s place. So, the individual has 2 × 1 = 2. Consequently, there are three pieces to this number, which are: 300, 90, and 2. One must connect those pieces with additional signs. Most noteworthy, the number in the expanded form is 300 + 90 + 2.
Solved Question For You
Q1 Which of the following statements is not in accordance with the expanded form?
A. It is a way of writing numbers so as to see the math value of individual digits
B. Here, the breaking up of a number takes place according to their place value
C. It refers to a way of expanding the scope and value of a number
D. It refers to a way of writing numerical values such that it breaks up the value into separate digits
A1 The correct answer is option C., which is “it refers to a way of expanding the scope and value of a number.” This is because the expanded form has nothing to do with expanding the scope and value of a number.