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What is the notation and numeration, place value, face value, and expanded form:
Notation and Numeration
Notation and numeration refer to the way numbers are represented and expressed. This includes the use of digits, symbols, and other mathematical notations to convey numerical information.
Place Value
Place value refers to the value of a digit depending on its position in a number. In the decimal system, each digit has a place value that is a power of 10.
*Ones place*: The rightmost digit, which represents the number of ones.
*Tens place*: The second digit from the right, which represents the number of tens.
*Hundreds place*: The third digit from the right, which represents the number of hundreds.
*Thousands place*: The fourth digit from the right, which represents the number of thousands.
Example: In the number 456, the place values are:
4 (hundreds place) = 4 × 100 = 400
5 (tens place) = 5 × 10 = 50
6 (ones place) = 6 × 1 = 6
Face Value
Face value refers to the value of a digit itself, regardless of its position in a number. In other words, it is the value of the digit without considering its place value.
Example: In the number 456, the face values are:
4 = 4
5 = 5
6 = 6
Expanded Form
Expanded form is a way of expressing a number as the sum of its place values. It involves breaking down a number into its individual digits and multiplying each digit by its corresponding place value.
Example: The expanded form of the number 456 is:
400 + 50 + 6
This represents the sum of the place values of each digit:
4 (hundreds place) = 4 × 100 = 400
5 (tens place) = 5 × 10 = 50
6 (ones place) = 6 × 1 = 6