Final answer:
The query pertains to the concept of place value of a number in Mathematics, explaining the relative value of digits in the hundredths place compared to the tenths place, and the manipulation of decimal points when multiplying or dividing by powers of 10.
Step-by-step explanation:
The concept in question here is place value of a number. Each digit in a number has a specific value based on its position relative to the decimal point. In the decimal numbering system, place values to the left of the decimal increase by multiples of ten (ones, tens, hundreds, etc.), while place values to the right of the decimal point decrease by divisions of ten (tenths, hundredths, thousandths, etc.).
For example, in the number 231.45, the '4' is in the tenths place, which means it represents 4/10 or 0.4. The '5' is in the hundredths place, representing 5/100 or 0.05. As stated, a digit in the hundredths place (like the '5' in 231.45) has 1/10 the value of the same digit in the tenths place because 0.05 is 1/10 of 0.5.
When multiplying or dividing by powers of 10, the decimal point is moved to the right or left respectively, and when there are not enough digits, zeros are used as placeholders. Moreover, after addition or subtraction, the number of decimal places in the answer should match the smallest number of decimal places in any of the original numbers. In multiplication and division, the answer should retain the number of significant figures from the original number that had the fewest.