How to Teach Decimal Place Value
As a teacher, I would first introduce decimal place value by exploring the relationship between decimal and rational numbers. I would explain that a decimal number is just a special kind of rational number where the denominator is always equal to ten. I would then ask students to think about what happens when we move the decimal point one place to the right. We are essentially multiplying the original number by ten. The number represented by each digit in a decimal number gets multiplied by ten when we move the decimal point one place to the right (Sowder, Sowder & Nickerson, 2017). For example, the number 12.345 becomes 123.45 when the decimal point is moved one place to the right. We can also see that this new number is just an estimate of the original number.
Next, I would ask students to think about moving the decimal point two places to the right. We are essentially multiplying the original number by one hundred. This is because the number represented by each digit in a decimal number gets multiplied by one hundred when we move the decimal point two places to the right (Sowder, Sowder & Nickerson, 2017). For example, the number 12.345 becomes 1234.50 when we move the decimal point two places to the right. Once again, we can see that this new number is just an estimate of the original number.
Conversely, I would ask students to think about what happens when we move the decimal point three places to the right. We are principally multiplying the original number by one thousand. This is because the number represented by each digit in a decimal number gets multiplied by one thousand when we move the decimal point three places to the right (Sowder, Sowder & Nickerson, 2017). For instance, the number 12.345 becomes 12345.00 when we move the decimal point three places to the right. Once again, we can see that this new number is just an estimate of the original number.
References
Sowder, J. T., Sowder, L., & Nickerson, S. D. (2017). Student Solutions Manual to accompany Reconceptualizing Mathematics for elementary school teachers. Macmillan Learning.
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Question 
How to Teach Decimal Place Value
How would you teach the notion of decimal place value to a class? How are decimal numbers related to rational numbers? When is a decimal number also a rational number?