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Chapter 4: Problem 10

Add. $$ 2.3+0.729+23 $$

Short Answer

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Step by step solution

01

- Align the Numbers

Write the numbers 2.3, 0.729, and 23 vertically, aligning the decimal points.
02

- Add Zeros for Clarity

For ease of addition, add zeros to match the number of decimal places. This converts the numbers to 2.300, 0.729, and 23.000.
03

- Add the Numbers

Start adding from the rightmost decimal place to the left. Begin with the thousandths place: add 0 + 9 + 0 = 9. Then proceed with the hundredths place: add 0 + 2 + 0 = 2. Next, add the tenths place: add 3 + 7 + 0 = 10, which places 0 in the tenths place and carries over 1. Finally, add the whole numbers: 2 + 0 + 3 + 1(carried over) = 6, followed by 2 + 0 + 3 = 5.

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Key Concepts

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

decimal alignment
When adding decimal numbers, aligning the decimal points is very important. This ensures that each place value (ones, tenths, hundredths, etc.) lines up correctly. Misalignment can lead to incorrect results. For instance, in the exercise given, we align the numbers 2.3, 0.729, and 23 vertically.

To do this, arrange the numbers in columns so the decimal points form a straight line down. This step helps us see which numbers are in the same place values, like the tenths or hundredths place. Aligning decimals makes the addition steps far easier and more intuitive.
carrying in addition
Carrying, also known as regrouping, often happens when the sum of digits in a column is 10 or greater. In our exercise, when we add the tenths place (3 + 7), we get 10. We write 0 in the tenths place and carry over 1 to the next higher place value.

Here鈥檚 how we handle carrying when adding decimals:
  • Start from the rightmost digit (smallest place value) and move left.
  • Whenever the sum in a column is 10 or more, place the right-most digit in that column and carry the left digit to the next column.
  • Add the carried number in the next column along with the other digits.
Practicing carrying in addition will improve your accuracy and speed when adding larger numbers or longer decimals.
adding zeros
Adding zeros to decimal numbers does not change their value, but it can make addition easier by ensuring each number has the same number of digits after the decimal point. In our example, before we added, we changed 2.3 to 2.300 and 23 to 23.000.

Here鈥檚 why this helps:
  • It ensures that each digit is correctly placed in its respective column (tenths with tenths, hundredths with hundredths, etc.).
  • It simplifies the addition process, making it clearer which digits to add together.
  • It prevents mistakes that can occur from misaligned numbers or overlooked place values.
Remember, adding zeros can be a useful strategy for clarity and accuracy when working with decimals.

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