How the Base 10 Number System Works

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Math Questions
Explain how the base 10 number system works. How would you teach the notion of place value to a class? How are decimal numbers related to rational numbers? When is a decimal number also a rational number?
Notably, fractions and decimals are related. And decimals are an extension of the base-ten system. In essence, integers written in base ten are technically decimals. In base-10, every digit of a number has an integer value between 0 and 9 depending on their position (Billstein et al., 353). As such, the places and of the numbers are rooted in the powers of 10 and each number is 10 times the value of the right digit.
In teaching the notion of place value to a class, a teacher should introduce the concept of ones, tens, hundreds as well as tenths, hundredths, thousandths, and so on depending on the position of every digit. In practice, a number like 25.92 has the position of every digit is: 2 with a value of 20, 5 with a value of 5. On the other hand, 9 has a value of 1/10th and 2 with 2/100th. Again, any number that can be expressed as a fraction is a rational number. Likewise, any decimal that ends after a number of digits is considered to be a rational number.
Explain the process of decimal multiplication and division. Explain the mathematical justification for moving the decimal point when performing decimal division.
The process of multiplying decimal numbers obtained by multiplying the value of whole numbers and dividing the ...