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Chapter 5: Problem 8

Perform the indicated operations. $$-8.365-0.9$$

Short Answer

Expert verified
-9.265

Step by step solution

01

Understand the Operation

This is a subtraction problem where you need to subtract 0.9 from -8.365. The operation can be written as: -8.365 - 0.9
02

Align the Numbers

Write the numbers vertically aligning the decimal points to help with the subtraction: -8.365 - 0.900
03

Perform the Subtraction

Subtract the digits in each column from right to left, starting with the thousandths place: -8.365 - 0.900 ____________ = -9.265 So, -8.365 - 0.9 = -9.265

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decimal subtraction
When subtracting decimals, the process is very similar to that of whole numbers. The main difference is the alignment of decimal points and managing digits to the right of the decimal. It's crucial to work methodically from right to left, ensuring each column lines up properly.
For example, let's consider the problem -8.365 - 0.9. Because we鈥檙e working with decimals, we take care to properly place the numbers based on their decimal points to avoid any mistakes.
negative numbers
Working with negative numbers can be tricky, but understanding the principle behind them makes all the difference. In essence, a negative number represents a value below zero. When we subtract a positive number from a negative one, it鈥檚 akin to moving further into the negative.
Take the problem -8.365 - 0.9 for example. Here, we start from -8.365 and subtract 0.9, making the end result even more negative. Thus, we get -9.265.
aligning decimal points
Aligning decimal points is essential for accurate decimal subtraction. Always make sure that the decimal points and each corresponding place value (units, tenths, hundredths, etc.) are lined up vertically.
In our problem, -8.365 - 0.9, we align as follows: -8.365 (the original number) is placed over -0.900 to clearly see where each digit stands in comparison. This alignment allows for easier and more accurate subtraction.
borrowing in subtraction
Borrowing in subtraction helps manage cases where the top digit is smaller than the bottom digit in a column. When subtracting -8.365 and 0.9, you may need to borrow if a digit in the minuend (the number we鈥檙e subtracting from) is smaller than in the subtrahend (the number being subtracted).
For instance, when subtracting 0.9 (which aligns as 0.900) from -8.365, we look at each column from right to left. We borrow from the nearest left column if needed to ensure each subtraction step is accurate. This might require adjusting adjacent digits to facilitate a clear subtraction process, ensuring the final answer, -9.265, is correct.

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