Place Value
Every digit in a number has a place value in mathematics.
The value represented by a digit in a number based on its position in the number is known as place value. Here’s an example of the relationship between the place or position of the digits in a number and their place value.
- Place value of 7 = 7,000,000
- Place value of 2 = 200,000
- Place value of 3 = 30,000
- Place value of 1 = 1,000
- Place value of 4 = 400
- Place value of 6 = 60
- Place value of 8 = 8
Expanded Form
In its expanded version we divide a number into place values, and then expand it to show the value of each digit. The expanded form of 438, for example, is written as:
Therefore, the expanded form of 438 is: 400 + 30 + 8
What Does the “ Expanded Form ” Mean?
In mathematics, an expanded form of a number is defined as a notation. It is a way of writing numbers to define the value of each digit. If the numbers are written using place value, it will create convenience in understanding large numbers for students. For example, the expanded form number 6834 is written as, 6000 + 800 + 30 + 4.
In this case,
6 – A place for thousands, i.e. 6000
8 – Hundredths place, namely 800
3 – Tenths place, which is 30
4 – ones place, which is 4
Face Value:
In a number, the face value of a digit is the value of the digit itself. Each digit has its own face value, regardless of whether the number is a single-digit, a double-digit, a three-digit, or any other number with multiple digits. Let’s look at some examples to help us understand the concept of “place value”.
- For the number 8,8 is the place value.
- For the number 57, the place values of 5 and 7 are 5 and 7 respectively.
- For 45921, the face value of 9 is just 9, even though the face value of the number 9 is 900, as it’s located at the hundredths place in the number 45921.
How to Write Numbers in an Expanded Form ?
Go through the steps below to write numbers in an expanded form:
Step 1: Find the standard type of number.
Step 2: Find the place value of a given number using the place value chart.
Step 3: Multiply a given digit by its location and represent the number in the order (digit × value of place).
Step 4: Finally, represent all numbers in the form of (digit × place value), which is an expanded number type.
Solved Expanded Form of Numbers Examples
Example 1: What is 45712 in the expanded form?
Solution:
Step 1: The standard form number is 45712.
Step 2: Now, the place value of the given number is:
4 – Ten thousand
5 – Thousands
7 – Hundreds
1 – Tens
2 – Ones
Step 3: Multiply the given number by its place value.
(i.e.,) 4 × 10,000,5 × 1000,7 × 100,1 × 10,2 × 1
Step 4: Expanded form of 45712 is, 40,000 + 5000 + 700 + 10 + 2
Example 2: What is 13682 in the expanded form?
Solution:
Step 1: The standard form number is 13682.
Step 2: Now, the place value of the given number is:
1 – Ten thousand
3 – Thousands
6 – Hundreds
8 – Tens
2 – Ones
Step 3: Multiply the given number by its place value.
Which gives us,
1 × 10,000,3 × 1000,6 × 100,8 × 10,2 × 1
Step 4: Expanded form of 13682 is, 10,000 + 3000 + 600 + 80 + 2
Example 3: What is 4792 in the expanded form?
Solution:
To write 4792 in expanded form follow the below steps:
Step-1: To express the number, use a place value diagram.
place value of 4 = 4,000
place value of 7 = 700
place value of 9 = 90
place value of 2 = 2
Step-2:Using the expanded form, write the number.
Expanded form of the number 4792 is, 4,000 + 700 + 90 + 2
Example 4: What is 615628 in the expanded form?
Solution:
Step 1: The standard form number is 615628.
Step 2: Now, the place value of the given number is:
place value of 6 = 6,00,000
place value of 1 = 10,000
place value of 5 = 5,000
place value of 6 = 600
place value of 2 = 20
place value of 8 = 8
Step 3: Expanded form of the number 615628 is, 6,00,000 + 10,000 + 5,000 + 600 + 20 + 8
An expanded form of a number is the division of numbers based on place value, such as, tens, hundreds, thousands, ten thousands, and so on. The number represented by the sum of each digit multiplied by its place is called the expanded number type.
Place value of 8 = 8,000
Place value of 4 = 400
Place value of 9 = 90
Place value of 1 = 1
Hence, the expanded form of the number 8467 is, 8,000 + 400 + 90 + 1
Any number that needs to be written in an expanded form must be identified by its place value first. Each number is multiplied by a multiple of 10 and then added together. Numbers in the expanded form are converted to the normal form by placing each digit in its proper location according to the place value.