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Chapter 5: Problem 110

In the following exercises, add or subtract. $$100-65.83$$

Short Answer

Expert verified
34.17

Step by step solution

01

Align the numbers

To subtract 65.83 from 100, first align the numbers by placing the decimal points directly above each other. Add trailing zeros to make the number of decimal places equal. It would look like this: 100.00 - 65.83
02

Subtract the decimals

Subtract the decimal place starting from the rightmost digit: 0.00 - 0.83. Since 0 is smaller than 3, borrow from the whole number part: 100 becomes 99, and the decimal part becomes 10. Subtract: 10.00 - 0.83 = 9.17
03

Subtract the whole numbers

Now subtract the whole number portion: 99 - 65. Do each digit starting from the right: 9 - 5 = 4, and 9 - 6 = 3. Thus, the result is 34.
04

Combine the results

Combine the whole number and the decimal subtraction: 34 (whole number part) + 0.17 (decimal part) = 34.17.

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Key Concepts

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

subtracting decimal numbers
When subtracting decimal numbers, it's essential to align the decimal points. This ensures that each digit in the same place value is subtracted correctly. For instance, when subtracting 65.83 from 100, align the numbers as follows:
100.00
- 65.83
Notice we added two trailing zeros to 100 to make it 100.00. This adjustment helps maintain a clear process while dealing with decimals.
Remember to start the subtraction from the rightmost digit and move left.
borrowing in subtraction
Borrowing in subtraction is a critical step when a digit in the minuend (the number from which you subtract) is smaller than the corresponding digit in the subtrahend (the number being subtracted).
Let's look at our example:
100.00
- 65.83
Start with the rightmost decimal digits: 0 - 3. Since 0 is smaller, we borrow 1 from the whole number part of 100, making it 99 and converting 0.00 into 10.00.
This allows us to proceed:
10.00 - 0.83 = 9.17.
Now, subtract the adjusted whole number: 99 - 65.
place value alignment
Aligning place values correctly is crucial when working with decimals. Ensure that each digit of the same place value (units, tenths, hundredths) lines up vertically. This prevents errors in calculation.
For example:
100.00
- 65.83
Digits at each place value (ones, tenths, hundredths) are directly aligned. Trailing zeros can help maintain this alignment. By ensuring proper alignment, you prevent confusion and make the subtraction process straightforward and accurate.

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