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Chapter 4: Problem 44

Subtract. $$ 45-0.999 $$

Short Answer

Expert verified
44.001

Step by step solution

01

Align the Numbers

To subtract, start by writing the numbers vertically, aligning the decimal points: \[45.0-0.999\]
02

Borrow if Necessary

Since the number under subtraction (0.999) has more digits after the decimal point, write 45 as 45.000 for easier calculation. \[45.000-0.999\]
03

Subtract Each Column

Subtract each column starting from the right: \[0-9 = -9 \text{ (borrow 1 from the next column)},\ 10-9 = 1\] \[10-9 = 1\] \[9-9 = 0\]Continuing this until the highest place value. \[44.001\]

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Key Concepts

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

borrowing in subtraction
When subtracting numbers, sometimes you encounter a situation where the top digit is smaller than the bottom digit. This is where 'borrowing' comes into play. Borrowing means you take 1 from the next left column to make the current subtraction possible.
For example, when subtracting 0.999 from 45.000:
- In the first column (to the right), you can't subtract 9 from 0, so you borrow 1 from the next column.
- This changes the current column from 0 to 10 and the next column by decreasing 1. Repeating this process until the highest place value helps you compute the final answer accurately.
decimal subtraction
Subtracting decimals might seem tricky at first, but it's straightforward if you handle it step by step. Here鈥檚 what you should do:
- Write down the numbers with their decimal points aligned.
- If necessary, add extra zeros to the end of the numbers to make sure they have the same number of decimal places.
- Subtract as you would with whole numbers, borrowing if needed.
For instance, in the exercise 45.000 - 0.999, after aligning the decimal points, you subtract column by column, borrowing when the top number is smaller than the bottom one. The key is to ensure each digit is properly aligned and to borrow correctly.
aligning decimal points
Aligning decimal points is fundamental in decimal subtraction. This ensures that each place value (units, tenths, hundredths, etc.) is correctly matched up, allowing for accurate subtraction.
- Start by writing the numbers in a column, making sure the decimal points are directly one above the other.
- If one number has fewer digits after the decimal, add zeros to make them match.
For example: in the problem 45.000 - 0.999, aligning decimal points guides you to correctly line up 45.000 on top and 0.999 directly below, ensuring that each digit is in its proper place for accurate subtraction.

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