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Understanding the concept of place value is essential when dealing with numbers, especially in their decimal form. In essence, place value tells us the value of a digit depending on its position within a number. For whole numbers, the place value of digits increases from right to left, with the rightmost position being the 'ones' followed by 'tens', 'hundreds', and so on.

When it comes to decimals, the same principle applies but in reverse. Directly to the right of the decimal point is the 'tenths' place, followed by 'hundredths', and 'thousandths'. So, in the number 0.672, the '6' is in the tenths place, the '7' is in the hundredths place, and the '2' is in the thousandths place. Each position represents a division by ten, so for instance, '7' in the hundredths place actually represents 7/100 or 0.07 in decimal form.

Decimal notation is a way of writing numbers that includes a decimal point to represent a whole number plus a fraction of a whole number. In decimal notation, the digits to the left of the decimal point represent the whole number, while the digits to the right represent the fractional part. This notation is critical when representing numbers smaller than 1, such as in the problem where we have to express 'six hundred seventy-two thousandths'.

In decimal notation, this is represented as 0.672, indicating that the number is smaller than one whole but more than zero. The leading zero before the decimal point emphasizes that we're dealing with a number less than one. Decimal notation allows for the precise representation of numbers and is widely used in scientific, financial, and everyday contexts.

When converting words to numbers, particularly in the case of decimals, it's crucial to understand not just the numeric value but also the context given by the wording. The term 'six hundred seventy-two thousandths' refers to a precise fraction. To convert it to a numerical decimal, one must first identify the base number, '672' in this case, and then place it within the context of the specified decimal place value, which is 'thousandths'.

Therefore, you begin with '672' and then adjust the decimal point so that '672' falls within the thousandths place. By inserting a decimal before '672', making it '0.672', we reflect the exact value denoted by the words. This process demands attention to both the numerical digits provided and how they are situated in relation to the decimal point.