Answer:
The digit 6 has a greater value than the digit 5 because it is in the place that is ten times as large. Similarly, the digit 5 has a greater value than the digit 4 because it is in the place that is ten times as large, and so on. Each digit's value is one-tenth as large as the digit to its left because each position is divided into ten equal parts.
Each digit has a different value due to the positional number system we use, known as the decimal system. In this system, the value of a digit is determined by its position or place within a number. Each position represents a power of 10, with the rightmost position representing the ones place, the next position to the left representing the tens place, the next position representing the hundreds place, and so on.
Let's take the number 3456 as an example. In this number, the digit 6 is in the ones place, the digit 5 is in the tens place, the digit 4 is in the hundreds place, and the digit 3 is in the thousands place.
The value of each digit depends on its position because each position is ten times as large as the position to its right. Going from right to left, each digit represents a multiple of ten times the value of the digit to its right.
For instance:
The digit 6 in the ones place represents 6 ones, which is its face value.
The digit 5 in the tens place represents 5 tens, which is 5 times 10 or 50.
The digit 4 in the hundreds place represents 4 hundreds, which is 4 times 100 or 400.
The digit 3 in the thousands place represents 3 thousands, which is 3 times 1000 or 3000.
So, the digit 6 has a greater value than the digit 5 because it is in the place that is ten times as large. Similarly, the digit 5 has a greater value than the digit 4 because it is in the place that is ten times as large, and so on. Each digit's value is one-tenth as large as the digit to its left because each position is divided into ten equal parts.
In summary, the positional decimal system assigns different values to each digit based on their position within a number, with each position being ten times as large as the position to its right and one-tenth as large as the position to its left.