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Chapter 4: Problem 14

Add. $$ 17+3.24+0.256+0.3689 $$

Short Answer

Expert verified
20.8649

Step by step solution

01

Align the Numbers

Align the numbers by their decimal points to ensure accurate addition. 17.0000 03.2400 00.2560 00.3689
02

Add from Right to Left

Start adding the numbers from the rightmost digit. 9 (from 0+0+0+9) 8+6 = 14, write down 4, carry over 1 4+5+2 = 11, plus 1 carried = 12, write down 2, carry over 1 7+2 = 9, plus 1 carried = 10, write down 0, carry over 1 1+1 = 2
03

Combine the Results

Combine all the additions and place the decimal point in the correct position. The final result is 20.8649.

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Key Concepts

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

aligning decimal points
When adding decimals, it's crucial to align the numbers by their decimal points. This ensures that the digits in each place value (ones, tenths, hundredths, etc.) line up properly. For example, with the numbers
  • 17 (or 17.0000 for alignment)
  • 3.24 (or 03.2400 for alignment)
  • 0.256
  • 0.3689
We align them as follows:
17.0000
03.2400
00.2560
00.3689Aligning the decimals like this makes it easier to add them correctly. Notice how you can treat 17 as 17.0000 for alignment purposes. Each position in the numbers occupies the same column, making the addition process clear and straightforward.
carrying over in addition
Carrying over in addition is important when the sum of two digits in a column exceeds 9. In such a case, you write down the rightmost digit and carry over the leftmost digit to the next column. For instance, if we start adding from the rightmost digits:

0 + 0 + 0 + 9 = 9
8 + 6 = 14, write down 4, carry over 1
4 + 5 + 2 = 11, plus 1 carried = 12, write down 2, carry over 1
7 + 2 = 9, plus 1 carried = 10, write down 0, carry over 1
1 + 1 = 2
This process ensures that each column is properly added, even if the sum exceeds 9.
place value in decimals
Understanding place value in decimals is crucial for accurate addition. Place value helps us to know the value of each digit depending on its position relative to the decimal point. Consider the number 20.8649. Here, the digit 2 is in the tens place, 0 in the ones place, 8 in the tenths place, 6 in the hundredths place, 4 in the thousandths place, and 9 in the ten-thousandths place.
When adding decimals:
  • Align the numbers by their decimal points.
  • Add each column starting from the rightmost decimal place.
  • Carry over to the next column if the sum exceeds 9.
Recognizing the place values will ensure that decimal points are kept in the correct position, ultimately yielding accurate results. The final result from our example is 20.8649, demonstrating the importance of correct place value in decimal addition.

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Most popular questions from this chapter

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