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Chapter 5: Problem 113

Explain how adding or subtracting decimals is similar to adding or subtracting whole numbers.

Short Answer

Expert verified
Align the numbers by decimal points, then add or subtract as with whole numbers, keeping decimal points aligned in the result.

Step by step solution

01

Align the Numbers

Whether you are adding or subtracting decimals or whole numbers, the first step is to align the numbers vertically so that the place values (ones, tens, hundreds, etc.) line up correctly. With decimals, make sure that the decimal points are also aligned.
02

Add or Subtract as Usual

Once the numbers are aligned, perform the addition or subtraction starting from the rightmost digit (the smallest place value) and moving towards the left, just as you would with whole numbers.
03

Place the Decimal Point

In the final step, after you've completed the addition or subtraction, ensure that the decimal point in the result is directly aligned with the decimal points in the numbers you were working with.

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Key Concepts

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

Aligning Numbers
When working with decimals, aligning the numbers is crucial for accurate calculations. This process is very similar to dealing with whole numbers, where you carefully align each digit according to its place value before performing operations like addition or subtraction.

Since decimal numbers might contain a different number of digits before or after the decimal point, a common practice is to write the numbers so their decimal points are vertically aligned. This ensures that each column contains digits of the same place value.

  • Align digits based on decimal point positions.
  • Add placeholder zeros if necessary, so each number extends to the same length if this aids alignment clarity.
Remember, aligning correctly prevents errors that may arise from mismatched place values.
Place Value
Place value is a foundational concept in mathematics, dictating the value of a digit based on its position within a number. Understanding place value is essential when dealing with both whole numbers and decimals.

With decimals, the numbers to the left of the decimal point represent whole units (ones, tens, hundreds, etc.), while those to the right represent fractional parts (tenths, hundredths, thousandths, etc.).

  • The digit immediately to the right of the decimal point is in the tenths place.
  • Each subsequent digit moves one place further to the right into hundredths, thousandths, and so on.
By comprehending the place value, you can add or subtract such numbers with precision, ensuring each digit contributes appropriately to the result.
Decimal Point Alignment
The alignment of decimal points is a critical step in performing operations with decimals. This process ensures that each digit is correctly placed relative to others based on its position in the number.

When adding or subtracting decimals:
  • First, align the decimal points vertically.
  • Then, place zeros as necessary to ensure that each number has the same number of digits after the decimal point.
  • This might involve adding zeros to the right in some of the numbers to simplify the operation.
Once aligned correctly, you can proceed with adding or subtracting just as you would with whole numbers.

Ultimately, the decimal point in your answer should align directly under the decimal points used in your initial numbers, maintaining the correctness of the result.

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