Place value is a fundamental concept in mathematics that refers to the value of each digit in a number based on its position. Understanding place value is essential for grasping how numbers are constructed and how they can be manipulated through various mathematical operations. When we talk about expanding numbers in terms of place value, we mean breaking down a number to show the value of each individual digit according to its position in the number.
Place Value
In a multi-digit number, each digit has a place value that depends on its position from right to left:
- The rightmost digit is in the ones place.
- The next digit to the left is in the tens place.
- The next digit to the left is in the hundreds place, and so on.
For example, in the number 5432:
- The digit 2 is in the ones place and has a value of 2.
- The digit 3 is in the tens place and has a value of 30 (3 tens).
- The digit 4 is in the hundreds place and has a value of 400 (4 hundreds).
- The digit 5 is in the thousands place and has a value of 5000 (5 thousands).
Expanding Numbers
Expanding a number involves expressing it as the sum of its place values. This helps in understanding the composition of the number and is a crucial step in performing arithmetic operations such as addition, subtraction, multiplication, and division.
For example, the number 5432 can be expanded as: 5432=5000+400+30+25432 = 5000 + 400 + 30 + 25432=5000+400+30+2
