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Understanding the concept of rounding is critical when estimating in mathematics, especially with decimal numbers. Rounding is a process by which we simplify a number to make it easier to work with, while still keeping it close to the original value.
When you're instructed to round to a certain place value, like to the nearest hundredth (which is two decimal places), you look at the number in the third decimal place. If this number is 5 or higher, you increase the second decimal place by one. If it's 4 or lower, the second decimal place stays the same.
For example: the number 0.1005, when rounded to the nearest hundredth, becomes 0.10 because the third decimal place (0) is less than 5. Similarly, 0.08261 rounded to the nearest hundredth is 0.08 for the same reason.

Arithmetic operations are the foundation of most mathematical calculations, encompassing addition, subtraction, multiplication, and division. When we talk about estimating sums, we're usually referring to simplified addition or subtraction. It involves combining numbers to find their total, or in the case of subtraction, finding the difference between them.
Estimation with arithmetic operations often requires the use of rounding beforehand, so numbers are easier to combine mentally. After rounding the numbers as our first step, we proceed to perform the arithmetic. For instance, after rounding 0.1005 to 0.10 and 0.08261 to 0.08, we perform the subtraction (0.10 - 0.08), which because of our previous rounding, results in an estimated sum.

Decimal subtraction is essentially subtraction involving numbers with decimal points. When subtracting decimals, it's crucial to align the decimal points vertically to ensure that each place value lines up correctly. This helps prevent errors during the subtraction process.
When dealing with actual calculations, as opposed to estimates, you subtract each digit in the corresponding place value position, borrowing from the next higher value when necessary. For instance, subtracting the original numbers 0.1005 and 0.08261, you would carefully subtract each digit in the tenths, hundredths, thousandths, and so on, yielding an actual sum of 0.01789.
This process can be more complex than simple whole number subtraction due to the presence of decimals and the need for precise alignment, which is why estimation through rounding can simplify the initial steps of the process.